Geometric Properties of Steel Components with Stability and Fatigue Risks Using 3D-Laser-Scanning

Abstract

Nowadays, 3D laser scanning technology is extensively employed in laboratory investigations of steel structural components, providing accurate geometric dimensions to reduce uncertainties caused by indeterminate geometry in experimental results. It is often used in conjunction with the Finite Element (FE) Method and analytical solutions, which are more accurate deterministic operators in the research on steel structures. However, establishing a common methodological framework for transferring or mapping 3D-scanned information into finite element models for complex steel structures with stability and fatigue risks remains an ongoing task. In light of this, this study has developed a 3D scanning platform capable of obtaining accurate geometric dimensions for various types of steel components. Different coordinate systems and point cloud mapping algorithms have been established for different types of components to construct actual finite element models with initial imperfections. The feasibility of the self-developed 3D scanning platform and finite element modelling has been validated through three experimental cases: weld details, steel girders, and cylindrical shells. The research findings demonstrate that the captured point cloud can be automatically processed and corrected using the developed algorithm. The scanned data can then be input into the numerical model using various mapping algorithms tailored to the specific geometric properties of the specimens. The differences between the experimental test results and the simulated results obtained from the 3D-scanned finite element models remain within a small range. The self-developed 3D scanning platform and finite element modelling technique effectively capture the actual dimensions of different steel components, enabling the prediction of their stability and fatigue risks through numerical simulations.

1. Introduction

Currently, considerable attention is being given to the development of more accurate deterministic operators, including methods such as the Finite Element Method (FEM) and analytical solution approaches. These approaches take into account the complex relationship between stability and fatigue strength, as well as the influences of initial conditions. Concurrently, it is essential to analyse the influence of various parameters such as material properties, geometry and initial imperfections on the stability capacity by means of these approaches. In general, the validation of the results has to be confirmed by experiments. The fatigue strength of welded structural components and the stability of steel structures such as thin-walled and shell structures are of major importance in steel structures. The buckling behaviour of steel structural components significantly depends on initial geometric imperfections [1,2,3], and the measured geometric imperfections are essential as predefined input values for the calculation using geometrically and materially nonlinear analysis with imperfections included (GMNIA) [4,5]. In general, geometric imperfections can be divided into two categories: global and local imperfections, which are the dominant causes of premature global and local instability or buckling, respectively. Most recently, Aktepe and Erkal [6] reviewed a large number of existing research results and publications concerned with the measurement, identification, prediction and modelling of geometrical imperfections in cold-formed steel components so as to provide useful information about the factors to consider in design and analysis. It was shown that the methodology for modelling geometric imperfections is of paramount importance and is largely dependent on the information available to model the imperfections in the geometry. Furthermore, in the case of welded structures, due to the discontinuous geometry of the weld seam, the stress field at the weld is usually singular, which is a primary factor that complicates the fatigue strength issues of welded joints in steel structures [7]. Traditional fatigue assessment methods are often based on the ideal geometry defined by the weld toe to describe welds, ignoring the influence of real geometric dimensions on actual stress concentrations and fatigue life predictions [8]. Therefore, an accurate investigation of these topics in the laboratory is required, as is the successful application of laser scanning technology to obtain the exact geometric dimensions [9,10]. Applying accurately measured geometric dimensions and initial geometric imperfections of the specimens in experimental investigations can significantly reduce the scatter of observed results. For example, geometric imperfections play a key role in the buckling of shell structures, which is considered one of the most difficult factors to predict for shell structures [11]. By accurately measuring the three-dimensional (3D) geometry of the cylindrical shell specimens, it is possible to precisely determine the load-bearing capacity of these shell specimens [12].

In order to determine the geometric dimensions and/or imperfections of specimens, numerous measurement methods are available, which, in principle, can be divided into two main categories: Contact methods and non-contact methods [13]. At the beginning of the decade and even before, a contact coordinate measuring machine was often used to record geometric imperfections [14]. These scanning systems are usually calibrated on a fixed platform and consist of a sonde attached to the end of a mechanical swivel arm. When the sonde touches the surface of the specimen, the scanner determines the spatial position of the sonde by measuring the location with the corresponding sensor. The recorded positions generate a point cloud that can be used to form a 3D model [15]. Contact methods based on physical movement are generally quite slow and restrict the geometry of the specimens and the size of the structural component to a specific range of lengths. Non-contact methods traditionally use telescopes and theodolites, as well as rulers or callipers, to measure total deviations at several pre-determined cross-sections of scanned specimens [16]. To overcome these limitations, some of the research teams have turned their focus to non-contact methods based on laser and structured light measurement technology. The principle of 3D laser scanning is that a scanner protrudes a laser beam onto a surface, and the reflected beams back to the scanner are measured and recorded. The laser beam can be projected onto the target object in three different ways: Point, Line and Plane. By measuring the distances and angles of the reflected laser beam, the scanner can create a point cloud of coordinates in three-dimensional space that represents the shape and contours of the scanned specimen. Structured light scanning is a similar technique, except that a few stripes of light are projected onto a 3D-shaped surface, creating single or multiple illuminated lines or patterns of blue light. The displacement of the stripes on the projected 3D surface provides the ability to capture point cloud coordinates for details on the surface of the scanned object [17].

Currently, 3D laser scanners are widely used in experimental investigations in steel structures to capture the geometric dimensions of specimens. In this decade, Zhao et al. developed a platform for measuring geometric imperfections of cold-formed steel members based on laser scanning technology [18] and proposed a novel method for feature recognition to distinguish and extract geometric properties, such as corner points and planes from target scanned specimens [19,20]. For Box-T beams with complex cross-section profiles and difficult-to-measure geometric imperfections, Zhang et al. [21] used a handheld 3D laser scanner to measure the entire geometric profiles of Box-T girders. More recently, Meng et al. [13] explained the typical 3D scanning workflow using a typical I-shaped structural steel profile specimen nearby. Additionally, numerous studies have utilised 3D scanning to obtain accurate weld details for evaluating the fatigue behaviour of welded joints. For example, Ghahremani et al. [22] used a handheld laser scanner to determine the geometric dimensions of treated welded joints. Niederwanger et al. [23,24] applied 3D laser scanning to obtain the real weld geometries and introduced the geometric information into the evaluation to reduce the scatter of fatigue life due to geometry variations for each weld of different specimens. More recently, Shojai et al. [25] investigated structural steel specimens of offshore wind support structures with pitting using a 3D scanner and analysed the influence of the pitting corrosion and related stress concentrations on the fatigue strength of the support structures. In the framework of experimental investigations in steel structures, especially for the determination of specimen geometries and the characterisation of geometric imperfections, the use of 3D scanning is discussed by means of application examples [26]. Handheld laser scanners prove to be simple and user-friendly in practice, but they are relatively expensive. Moreover, the accuracy as well as the algorithms embedded in them are not fully transparent for the user. The efficient, simple and meaningful transfer of the measured point cloud information into the finite element (FE) model is still a challenge for structural components of different sizes, such as steel beams of several metres or weld seams of a few millimetres.

In this paper, a self-developed 3D laser scan platform based on laser triangulation is used to capture specimen dimensions using point clouds. The specimens include steel beams with web openings to investigate buckling behaviour [27], cylindrical shell specimens with a diameter of up to 1.6 m [28], and weld seams of the cross-weld specimen. The procedures for post-processing of the point clouds and the general steps for transforming the point cloud information into an FE model are presented in detail. Finally, the test results are compared with the simulation results.

2. Principles of 3D Scanning and Scan Platform Design

This section first explains the basics of 3D scanning and introduces the functional principle of the self-built 3D scanning platform. Then, it describes in detail the process by which the 3D coordinates of the point cloud can be optimally generated for the experimental specimen.

2.1. Three-Dimensional Laser Scan Platform with Different Coordinate Systems

Using a laser scanner for 3D measurement involves two basic tasks: (i) the measurement of the spacing between the distance sensor and the measured object; (ii) the determination of the relative movement between the distance sensor and the tested object and the accurate recording of the path of the movement. The determined distances and paths of movement form a point cloud of coordinates in three-dimensional space that represent the shape and contours of the scanned specimen. According to the previously explained principles, a fully automated 3D scan platform design idea is proposed. During the scanning process, two stepper motors with transmission devices such as threaded spindles enable the relative movement between the distance sensor and the object to be measured. By measuring the clearances through the distance sensor and the parameters of the two stepper motors in relation to the current position of the distance sensor, a three-dimensional coordinate system can be created to determine the relative positions between the measured points.

To enable the synchronised operation of these hardware components, an Arduino Uno board is used to control the scanning process and set up the data transmission, according to Figure 1. The control programme is written in C++ using the Arduino (IDE) software (https://www.arduino.cc/en/software) and uploaded to the Arduino Uno board via the USB serial port. By setting predefined parameters in the control program, such as the speed of the stepper motors, the frequency of the analogue voltage readings from the stepper motors and the laser distance sensor, different dimensions of the scanned specimens can be set, and the resolution of the point cloud can be varied. The highest resolution of the stepper motor and corresponding driver is 8000 steps per revolution. One rotation of the thread moves the screw nut by 5 mm. This means that the parameter accuracy of the stepper motor is 5/8000 mm. With appropriate parametric settings, such as the stepper motor speed being 200 rpm and the scanned point cloud grid being 10 mm × 10 mm, high accuracy can be achieved at comparatively high scanning speeds, providing an optimum balance between speed and accuracy of the scanning process. The position of a spatial point is first represented using analogue signals from a distance sensor and a stepper motor.

These analogue signals are converted into digital signals by an analogue/digital conversion circuit within the Arduino Uno board. For data saving and post-processing, the digital signals must be communicated to the PC via the USB serial port. Here, a programme developed in Matlab^® 2022b automates this procedure. When performing 3D scans of the measurement specimens, the selection of the appropriate 3D coordinate system plays a major role, as this has a direct influence on the accuracy of the scan results, the complexity of the processing and the user-friendliness for subsequent applications. The determination of the scan path and the coordinate system depends on the practical requirements, the properties of the scanner as well as the geometry of the specimen to be scanned.

From a theoretical point of view, three parameters of orthogonal coordinates can describe the positional information of a point in three dimensions. Thus, these scanning systems have to provide only three parameters at any time point. By repeating with the predefined interval, the parameters for generating a three-dimensional coordinate point cloud can be obtained. In this paper, the position values of the two stepper motors and the distance sensor are adopted as three return parameters of the developed 3D scan platform. These parameters can be determined by simple mathematical operations to obtain the required point clouds. By employing this approach, two scan measurement systems can be established based on the characteristics of the scanned specimen and the scanning method, utilising cylindrical coordinates and Cartesian coordinates as foundations. Figure 2 presents the scan platform set-up established in this study for cylindrical circular shells.

The initial geometric imperfections in the web of a steel beam can be described as the difference between a point on the web and the corresponding point on perfect specimens. It should be noted that due to the scanning process and coordinate representation, 3D scanners based on the cylindrical coordinate system will not be suitable for capturing complete point cloud data from large flat surfaces such as the web of a structural beam. For steel structural component specimens that are relatively flat and without a large area of curvature, a measuring system on the plane of the Cartesian coordinate system (as shown in Figure 3) is suitable, as any two axes can form a plane in this coordinate system. This makes it possible to measure the initial geometric imperfections of the web in the structural beam specimen with this scanner system. In order to enhance scanning efficiency and data acquisition, two distance sensors will be employed. Figure 3 illustrates the approximate trajectory of the laser distance sensor as it moves along the web of the beam specimen.

As illustrated in Figure 4, the geometric imperfections at the welding joint can be captured by extracting geometric features. Specifically, the thickness of the weld seam is determined through an analysis of the weld toe and leg lengths, as well as the dimensions of the transition area. Although all four welds of the cross-welded specimen can be obtained simultaneously by turning the specimen, rotation of the specimen will cause the base steel plate to obscure the weld detail. The 3D scanner, which is based on a Cartesian coordinate system and, as shown in Figure 3, allows horizontal and vertical movement of the distance sensor. Therefore, this scanning procedure is, in general, suitable for scanning steel structural girders as well as for welded specimens based on the baseplate cross-section. The generation of a Cartesian coordinate system for steel beam and weld joint specimens is comparatively uncomplicated, as the three parameters returned by the measuring system correspond to three orthogonal coordinate axes.

2.2. Verification and Calibration of the 3D Laser Scan Platform and Error Analysis

The 3D scanning platform utilises the Panasonic^® HG-C1200 laser sensors (Panasonic Industry Co., Ltd. Osaka, Japan)to obtain the distance between the measuring device and the specimen via non-contact methods. According to product instructions, the measurement range and accuracy of the laser distance sensor are ±80 mm and 0.2 mm, respectively. Note that the analogue/digital conversion circuitry on the Arduino Uno board only provides 10 bits of resolution, i.e., 1024 different values. Therefore, the accuracy of the entire measurement system is limited to the range of the maximal value between 0.2 mm and $160/{10}^{10}=0.156$ mm at the hardware level. Nevertheless, it should be noted that the actual accuracy may deviate from the theoretical accuracy of a 3D scan platform. Various factors during the scanning process can influence the actual accuracy, such as the environmental conditions, the stability and reliability of the scan platform, the calibration, the reflection behaviour of the scanned object and possible measurement errors.

To investigate the actual accuracy and working reliability of the 3D scanner, a high-precision aluminium plate polished with abrasive paste, which can be considered almost completely flat, is used as a perfect reference scanning specimen, as shown in Figure 5. By analysing the scanned point cloud results, it can be clearly seen that there are noticeable differences in the measured laser sensor value between the two different sensor movement directions on the 3D scanning platform based on the Cartesian coordinate system. This is probably due to the fact that the stiffness of the horizontal linear guide is not infinite, and as the laser distance sensor accelerates and decelerates, the slight distortion of the horizontal guide is not completely consistent in the two directions of motion, which results in a difference in the sensor measurements. In order to overcome the hardware shortcomings of the scanning platform, the measurements in the two directions are checked separately, and the values of the laser distance sensor in the two directions have to be corrected for a difference of about 0.5 mm in the post-processing of the point cloud data.

For the verification of the actual accuracy of the 3D scanner, the deviation of the original scanned data compared to the reference plane of the perfect specimen is taken into consideration. In this paper, the uncertainty band of 95% probability (quantile) is employed to determine the measurement accuracy. To graphically illustrate this estimate of accuracy and confidence interval, a histogram of the scanned results is plotted, and the mean value and the boundaries of the 95% confidence level are marked on the graph, as shown in Figure 6. From the diagram, it can be seen that the confidence interval is [−0.221, 0.221], which means that the actual accuracy of the scanner is about ±0.22 mm. The measurement accuracy is close to and slightly greater than the described theoretical accuracy.

3. Experimental Investigation with 3D Scan Platform

This section presents application examples and 3D scanning results from experimental investigations on the stability and fatigue tests of steel components. The analysis encompasses the determination of geometric properties and the characterisation of geometric imperfections. The post-processing of the recorded point clouds of these specimens is also illustrated.

3.1. Three-Dimensional Scanning of Specimen Geometries

To accurately investigate the buckling behaviour and load-bearing capacity of cylindrical shell specimens and compare them with the experimental results, a large number of cylindrical shell specimens were scanned, as shown in Figure 7. Two Panasonic^® laser sensors are used to measure the inner and outer walls of the test specimens. In order to achieve the high precision of the measurements, the predefined driver software controls the stepper motor so that the specimen is accelerated within one minute so that it rotates once every 8 s and then rotates at a constant speed. Simultaneously, the vertical stepper motor is also accelerated to a constant movement of 1 mm every 8 s within one minute. This causes the measured points to be in a spiralling shape. Each scanning process requires approximately 2.5 h to record all geometric dimensions. The spatial resolution of the measured points is 1 mm in the axial direction and 1.25 mm in the circumferential direction.

For the investigation of the shear buckling behaviour of steel girders with web openings [27], the initial geometric imperfections of the entire web were analysed based on the real geometric dimensions of the out-of-plane with 3D scanning. Due to the large dimensions in the length direction, the steel beam was scanned in segments in an upright position, as shown in Figure 8a. Two distance sensors are employed to obtain a large amount of data. This means that each sensor obtains a point cloud with a scanning density of $2\ast 10 \mathrm{mm}$ by the end.

In order to more accurately investigate the fatigue behaviour of welded components, it is necessary to precisely determine the weld thickness of the specimens using 3D scanners. In practice, it is difficult to scan all four welds at the same time with sufficient accuracy due to the geometry of the weld seams for cross joints. A solution to overcome these difficulties is as follows: first, scan one side of the welded specimen and then capture the other side. In order to ensure that the weld seams match on both sides during scanning, a small piece of marker is placed on the weld joint specimen (s. Figure 8b). This will be considered in the post-processing of the scanning results.

3.2. Post-Processing the Point Cloud

The main purposes of post-processing the point cloud are reducing measurement noise and merging the point cloud data or removing irrelevant data. Due to the different geometries and sizes of the specimens, as well as the different scanning methods, it is necessary to use various algorithms for the post-processing of the point cloud data. It includes the correction of relative positions, the suppression of noise and merging, as well as deleting point clouds. In this way, the distribution of the point clouds is reconstructed more precisely to better match the real steel specimens.

The first task in sampling from point clouds is to extract undisturbed point cloud data. During the scanning process, the relative position of each individual specimen to the scanner varies within a reasonable range, so it is difficult to automate accurately by using some mathematical algorithms. Hence, manual removal of those point clouds that are not part of the sample is recommended. For maximal noise reduction, a conservative approach is required to obtain the largest possible number of relevant points from the scanned specimens. Nevertheless, due to the large number of measured values acquired, minor human errors have no significant influence on the final outcome. The subsequent steps vary depending on the scanning method applied as well as the differences in geometry and size of the individual specimens.

3.2.1. Case Study 1: Cylindrical Shell Specimen

The most important part of establishing the cylindrical coordinate system is finding the centre of the cylinder to ensure the correct relative position of all scanned points. During the scanning process, physical discrepancies can often occur that influence the constancy of the relative position between the target object and the 3D scanner. For example, it is basically impossible to place the central axis of the cylindrical shell specimen coincident with the centre of the rotating table of the 3D scan platform. Moreover, maintaining the axis of the shell specimen completely perpendicular to the plane of rotation is a challenging task with great difficulty and limited benefit. In order to minimise this measurement error, a linear regression algorithm can be employed to perform the curve fitting of the average distance between the points of each scanning series and the laser distance sensor, as shown in Figure 9. The slope of this fitted curve is utilised to smooth out all data points, aligning the distribution of the point more closely with the real testing specimen. The values for the angle $\mathit{\theta }$ and the height $\mathit{h}$ in the cylindrical coordinate system can be determined by using the recorded steps of the stepper motor. The following equation shows how this is possible:

(1)$\mathit{\theta }=\Delta \mathit{s} \times \mathit{N}\times {\mathit{\lambda }}_{\mathit{\theta }}$

(2)$\mathit{h}=\Delta \mathit{s} \times \mathit{N}\times {\mathit{\lambda }}_{\mathit{h}}$

where the step resolution of the stepper motor $\Delta \mathit{s}$ is the minimum rotation angle represented by each step change. $\mathit{N}$ is the current position of the stepper motor. $\mathit{\lambda }$ represents the rotation angle or height values per step.

The algorithm for determining the radius of the scanned specimen is based on the design circumference of the cylindrical shell. The specimens are rolled and welded with steel plates, which allows the circumference of the specimen to be considered as a constant value. The flow chart for this algorithm is shown in Figure 9. The principle of the algorithm is to employ a mathematical relationship whereby the radial displacement of the distance sensor is equal to the sum of the horizontal distance between the measurement point and the polar axis and the spacing between the distance sensor and the measurement point, as shown in Figure 9. First, a small value is assumed for the radial distance of the distance sensor, which in this paper is equal to the design radius. Then, this value is gradually increased through a loop, and the average horizontal distance of all measurement points to the polar axis is retraced using the above relationship. The loop will end as this value reaches the predefined design radius. Through this procedure, it is possible to derive the relative position of the longitudinal axis of the point cloud and to create a cylindrical coordinate system for the scanned specimen.

In general, the point cloud data of shell specimens arranged in the cylindrical coordinate system have undergone an adjustment of the relative positions of the data points during the establishment of the coordinate system. After removing irrelevant scan points manually, the point cloud can be used directly for further investigations. To prepare the transfer of the point cloud information, the transformation of the cylindrical coordinate system into a Cartesian coordinate system will be carried out afterwards. In addition, there are two algorithms to further smooth the point cloud and compress its data size. It is possible to unfold the measured point cloud onto a surface and then approximate it using surface fitting techniques, such as the Fourier series [29]. The level of data simplification, smoothing and compression depends on the number of terms in the fitting equation. For high densities of point cloud grids, a nearly error-free point cloud with the desired density can be generated. By combining the measured point cloud and the nearly error-free point cloud using mapping, a large amount of scanned data is used optimally and at the same time, the density of the point cloud grids will be reduced, which leads to a decrease in noise.

3.2.2. Case Study 2: Steel Beam with Web Openings

Segmented scanning is used due to the length of the specimen for the steel structural girders with web openings. Thus, the post-processing of the point cloud of the specimens is divided into two steps: first, the noise reduction and equalisation of the point cloud of each sub-segment, and then the merging and fusing of the point clouds for each two sub-segments. Since the motion plane of the distance sensor cannot be changed arbitrarily, the scanned plane of the specimen is kept roughly parallel to the plane of the path in order to be scanned during scanning. Consequently, the point cloud represented in the Cartesian coordinate system has inclinations in the two main axis directions on one of the planes. In order to modify the coordinates of the measurement points, it is necessary to perform some curve fitting based on linear regression. It is necessary to adjust the scanned points in both directions so that the distribution of the point cloud aligns more closely with the actual specimens. Figure 10 shows the inclinations in the longitudinal direction before the adjustment and the state after the improvement. The point clouds obtained from both sensors are merged after processing by aligning them at the geometric centre of the point clouds.

The segmented point clouds are merged in the subsequent processing phase to create a complete point cloud of the web, taking into account the length of the web and the position of the stiffener in the middle of the steel beam. The required overlap length at the two ends of the point clouds is simply determined mathematically by addition and subtraction. It should be noted that in processing each of the three segments of the point clouds individually, all of the corresponding coordinates must also be modified. This will help to ensure that the point clouds can be successfully connected. Moreover, due to manufacturing tolerances, the steel girders may deviate from the dimensions in the design drawings. A certain tolerance in the connection of the point clouds is acceptable.

3.2.3. Case Study 3: Welded Specimen

The post-processing of the point clouds for the welded specimen is quite similar to the one for the steel girder specimen due to the identical scanning procedures. The scan method for weld details determines the procedure for post-processing the point cloud data: At first, noise reduction and correction are performed for the scanned data of the A side of the point cloud. Then, the point cloud of the B side will be processed in the same way. To merge the point clouds of both sides of the welded specimen as well as the point clouds acquired by both sensors, the geometric centre points of the marker point clouds are aligned in the respective point clouds. Figure 11 shows the post-processing workflow for the point cloud of the specimen of weld joints. The quality of the connection is verified by observing the merging of the point clouds of the marker. The overall results are shown in Figure 12. The successful merging of the point clouds is clearly accomplished.

4. Numerical Modelling and Comparing with Experimental Results

4.1. Numerical Modelling Based on Scanned Point Clouds

In order to input the scanned geometric dimensions into numerical models for analysis, two main methods are available: generating 3D solid or shell elements from the original point and transferring point cloud information into numerical models by mapping algorithms. However, in essence, the mapping-algorithm-based approach is more general as it simplifies the scan results into normal input quantities parallel to the geometric dimensions and can completely disconnect from the limitations of meshing and element types. The implementation of the scanned information into numerical models can be easily completed using any commercial FE software. In this paper, some examples are presented based on the combination of Abaqus^® 2022 and Matlab^® 2022b Due to the internal data structure and API of Abaqus^® and by using the Python script interface, it is possible to write the necessary code. This will facilitate the access and editing of the coordinate data of the “Parts” in the FE model. Firstly, a perfect FE model will be defined in Abaqus^®, which is exactly matched to the corresponding specimens of the steel component. Then, the coordinates of the nodes are extracted from the “Parts” of the FE model using Python scripts in Abaqus^®, which have to be adjusted. In Matlab^®, the measured point data and the node information of the FE model are recorded. Then, a mapping relation is established between the measured points and the corresponding nodes in the FE model to modify the node coordinates. Finally, the node information is reimported into the FE model using Abaqus^® scripts to successfully import the geometric properties from scanning results into the numerical model. In the following, different algorithms for the mapping of point clouds are presented based on three different features of steel specimens.

4.1.1. Inverse Distance Weighting Interpolation Method

Usually, the positions of the measured point cloud are different from the node positions in the numerical model of the cylinder shell specimens. Furthermore, the point density in the measurements with 3D scans is significantly higher than the node density in the FE model. Consequently, the coordinates of the nodes in the FE model have to be modified by a mapping relationship to accurately represent the real measured initial geometric imperfections. For this procedure, the inverse distance weighting method proposed by Castro et al. [30] is used. This approach is based on the distances used for interpolation. At first, the geometric centres of the scanned point cloud and the node are aligned to the origin of the cylinder coordinate system (s. Figure 13). For each nodal point in the FE model, the distance to the neighbouring measured points is determined. Based on the reciprocal distance, the weights are calculated to ensure that nearby measured points have an appropriate influence on the FE nodes. Using the coordinates of the measured points and the corresponding weighting factors, the weighted average radial deviation—namely, geometric imperfection—can be calculated. Detailed instructions for calculation and equations can be found in the literature [1]. Figure 14 shows the ideal cylindrical shell and the FE model with initial geometric imperfections with 10 times magnification.

4.1.2. Surface Fitting Procedure

As mentioned above, there is also a mapping algorithm based on the surface fitting method that can be used as a solution for transferring information from the scanned results. The basic idea of these approaches is to approximate the information of the scanned point cloud to a definable two-dimensional (2D) surface equation by fitting techniques. Owing to the fact that cylindrical shell specimens have periodic properties in the circumferential direction, many researchers preferred to employ the Fourier series as a predefined 2D function. A general procedure is to deconvolve the point cloud for the cylindrical shell along the circumferential direction and then apply a 2D surface function to fit and approximate the original scanned results, as shown in Figure 15.

First of all, the measured point cloud of the cylindrical shell specimen is cut out along an axial position in Matlab^®. Then, a corrugated surface is generated along the circumferential direction and the axial direction. In order to replace the information of the scanned point cloud with fitting equations, a specific function of the 2D surface has to be fitted over the entire area of the point cloud. The radial deviation is calculated by the equation of the fitted result using the axial and circumferential coordinates. This method corresponds to the description of the initial geometric imperfections in the web of a steel girder. For the webs of steel beams, the initial out-of-plane deformation can be taken into account as a geometric imperfection. The further procedures are similar to the previous description and illustrate the FE model of the steel girder with and without geometric imperfections in the web in Figure 16.

4.1.3. Local Refinement Procedure

For some special details, especially for transitions between two or more surfaces, such as weld seams, it is difficult to efficiently and accurately transfer the scan results to the numerical model using the two methods described previously. For this reason, a procedure is proposed that analyses the geometric properties of the weld seam and maps them to local nodal zones of the FE model. This algorithm presents the treatment of fillet welds on the welded specimen.

For the evaluation of such weld joint details, the main aim is to divide the point cloud first into strips with a defined size (e.g., 5 mm width) along the width direction of the specimens and subsequently to perform a 2D-transformation of each strip, where the influence of the width direction is ignored. This changes the task of finding the intersection point of two curves into two dimensions. In order to emphasise the local influence and reduce the influence of the global point cloud on the results, a user-defined limit value is assigned to the distance between the scanned point and the intersection point. The point cloud outside the limiting region is excluded from the subsequent curve fitting analyses. The obtained 2D point cloud that is used in the fitting calculation essentially consists of two components, namely the part of the weld that coincides with the quadratic curve and the point cloud that is close to a line describing the base material of the steel plate. The intersection of the two curves is considered the boundary between the weld and the steel base plate. An automated loop will subsequently be employed to determine the size of every stripe from each weld, as shown in Figure 17. Finally, the coordinates of the FE nodes in the area of fillet weld are scaled in a proportion corresponding to the calculated weld size for a more uniform mesh distribution in Figure 18.

4.2. Comparison of Numerical Simulation and Experimental Results

In this paper, the scanning results are used to minimise the geometric discrepancies between the numerical model and the actual specimen. This enables more accurate predictions of numerical results for steel structural components with stability and fatigue risks, as compared to the experimental investigations. After the cylindrical shell specimen is scanned to generate the point cloud, it is subjected to an axial compression test to determine the bearing capacity under compressive force. The detailed experimental procedure can be found in the recent literature [28]. Figure 19 shows the axial load versus end-shortening relationship of the experiment and FE simulation with a time-dependent explicit dynamic method in Abaqus^® for one of the shell specimens. The outcomes show that the simulation results are highly consistent with the experimentally recorded values, especially for the overall stiffness of the specimen, which means the ratio of load to vertical deformation. Besides this, the discrepancy in maximum buckling load remains at around 4%. It is not easy to achieve such a small difference for a thin-walled cylindrical shell specimen with a radius-to-thickness ratio of approx. 800. However, significantly larger differences are found in the post-buckling phase, which may be due to the inability of the numerical analysis to fully simulate the boundary conditions in the experiment, as well as the high sensitivity of cylindrical shell buckling to initial geometric imperfections.

I-section girders with web openings, designed to accommodate pipes in buildings and bridges, usually suffer shear buckling failure due to the high slenderness of the web and the corresponding openings of thin-walled webs [27]. Thus, the effect of an all-around reinforcement with a hollow section of the web opening is investigated in three-point bending tests. The information on the geometrical imperfections of the scanned web is mapped into the numerical model by the proposed methods. The comparison results between experiments and FE simulation with GMNIA in Figure 20 indicate that the difference in the ultimate capacity of three-point bending girders is slightly less than 5%. Nevertheless, there is a significant difference in the stiffness of the specimen and the vertical load applied when the displacement of the mid-position of the steel girders is in the range of 3 to 10 mm. The possible reason can be attributed to the fact that the residual stress near the weld in the specimen was not considered in the numerical model.

As of today, there is a requirement for a methodology for fatigue strength assessment that is detached from the notch cases of welded structural details and is universally and quickly applicable, removing existing technical barriers in the field of fatigue life evaluation. The feasibility of fatigue analysis of welded components based on strain–life (E-N) curves using numerical methods is demonstrated in a research study. To analyse the influence of weld residual stress and weld leg dimensions on fatigue strength, welding simulation and 3D scanning technology were used to introduce residual stress and real weld sizes, respectively, into the numerical model. Figure 21 presents the results of the experimental test and numerical analysis. Furthermore, in addition to the limited number of obtained results, the Woehler line, fitted to the data, is also incorporated into the diagram. The presented data show that the E-N curve method with the Morrow mean stress correction model can overcome the limitations of existing methods and is a promising area of research for fatigue analysis. The utilisation of 3D scanning to obtain true geometric dimensions, along with the proposed algorithm, provides a significant contribution to this field of research.

5. Conclusions

This paper illustrates a common analytical framework for mapping point cloud information into numerical models based on spatial relationships, thereby integrating 3D laser scanning technology with FE modelling. Through meticulous experimentation and methodological development, the study has shown that the advanced scanning platform developed is capable of capturing accurate geometric dimensions and imperfections of a variety of steel components, offering significant improvements in the predictive capabilities of numerical simulations for stability and fatigue risk assessments in steel structures. Different coordinate systems are developed within the scanning system to ensure accurate scanning dimensions for different types of specimens in steel structures. Through the investigation of three kinds of specimens, namely weld details, steel girders and cylindrical shells, the stability and fatigue behaviour of steel structural components are examined. Post-processing procedures for the obtained point clouds are presented, including the construction of a refined FE model and the establishment of the spatial relationship between FE nodes and point clouds. This allows for simplification of the geometric dimensions obtained from the scanning process by accounting for coordinate deviations of the FE nodes. Finally, the processed point cloud information is integrated into the numerical model using advanced mapping algorithms.

Through comparative experimental investigations, the results affirmed that automatic processing and correction of the point cloud with the developed algorithm, followed by the application of tailored mapping algorithms, enable a high-fidelity transfer of scanned data into the numerical model. By utilising the point cloud data to include these imperfections in FE models, the study has contributed to reducing the variability in observed outcomes and enhancing the reliability of stability and fatigue strength predictions. The comparison between the experimental findings and the simulated results derived from 3D-scanned FE models demonstrated a congruence within a narrow margin, indicating that the approach could reliably predict the performance of different steel components. Furthermore, research has addressed the technical difficulties of translating 3D scan information into FE models for complex steel structures. The detailed study of geometric imperfections and their influence on stability and fatigue risk provides valuable insights into material behaviour under practical conditions, thereby providing an empirical basis for experimental investigation on structural specimens of steel structures. By demonstrating the practicality of the developed scanning platform, the study also provided a comprehensive methodological framework for transforming scanned data into actionable FE model inputs. This development holds promise for a wide variety of applications, including, but not limited to, the accurate characterisation of welded joints and the buckling analysis of thin-walled structures. Moreover, the integration of 3D scanning methods, which accurately capture the geometric dimensions of specimens before and after testing, with Digital Image Correlation (DIC) techniques for full-field measurement of displacement and strain on the specimen surface, forms a comprehensive system for geometric feature perception during experimental procedures. This advanced approach to measurement and acquisition provides researchers with a deeper insight into the mechanical behaviours of structural components during experimental studies.

Author Contributions

Conceptualization, Z.L.; methodology, Q.Z. and F.S.; software, Q.Z.; validation, J.W. and H.P.; formal analysis, F.S.; investigation, Q.Z. and J.W.; resources, Z.L.; data curation, Q.Z.; writing—original draft preparation, Z.L., Q.Z. and F.S.; writing—review and editing, J.W. and H.P.; visualization, H.P.; supervision, Z.L.; project administration, Z.L.; funding acquisition, Z.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to project sponsor reasons.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures

Figure 1. Schematic representation of the 3D scanning process.

Figure 2. Scan platform set-up for cylindrical coordinate system.

Figure 3. Scan platform set-up for Cartesian coordinate system and corresponding scan path.

Figure 4. Illustration for determining the weld thicknesses (a: thickness of the weld seam/Effective throat/Theoretical throat; b,c: legs).

Figure 5. Verification with aluminium plate polished with abrasive paste.

Figure 6. Histogram of measured values and 95% confidence interval.

Figure 7. Measurements of the cylindrical shells with 3D scanner [28].

Figure 8. Measurements of the experimental specimens with 3D scanner; (a) steel beam; (b) weld joint specimen.

Figure 9. Representation of the modification of the point cloud of cylindrical shells.

Figure 10. Combining of several scanned segments.

Figure 11. Algorithm workflow for post-processing of the point cloud of the weld joints.

Figure 12. Post-processed point cloud for weld joint.

Figure 13. Sketch of the inverse distance weighting interpolation method.

Figure 14. Comparison of FE models between the real specimen and ideal model.

Figure 15. Scan results and fitted surface of radial deviation of cylindrical shells.

Figure 16. Out-of-plane deviation and FE model for webs of steel girder.

Figure 17. Schematic presentation of the local refinement procedure.

Figure 18. Illustration of the point cloud post-processing of the weld joint specimen (left) and modelling FE model (right).

Figure 19. End-shortening versus axial load of cylindrical shell from numerical simulation and experiment.

Figure 20. Mid-span displacement versus vertical load of steel grider from numerical simulation and experimental test.

Figure 21. Comparison of fatigue curves from numerical simulation and experimental data for weld joints.

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