System and method for estimating nominal stress using finite element calculated stress

Abstract

The systems and methods described herein are configured to use finite element (FE) stress calculations to estimate nominal stress without manual calculations, particular grid density requirements, or identification of particular geometric parameters, such as sheet thickness. The systems and methods described herein can be used to identify nominal stresses in welded structures and components, and also non-welded components having stress concentration due to other reasons. The systems and methods described herein also allow for utilization of readily available FE stress results in a consistent manner, as well as providing user feedback regarding the accuracy of nominal stress approximations. In addition, the systems and methods described herein are generally faster and less error-prone than conventional techniques, and are relatively insensitive to the grid density of FE stress calculations.

Description

This application is a divisional application of the patent application with the filing date of October 1, 2019, application number 201980070854.8, and title "Systems and Methods for Estimating Nominal Stress Using Stress Calculated by Finite Elements".

[0001] Cross - reference to related applications This application claims the priority and benefit of U.S. Provisional Application No. 62 / 751,186, filed on October 26, 2018, entitled "Systems and Methods to Estimate Nominal Stress Using Finite Element Calculated Stress", which is hereby incorporated by reference in its entirety for all purposes. Background of the Invention

[0002] This disclosure generally relates to the estimation of nominal stress in welded structures and components or in non - welded components having stress raisers for other reasons. More specifically, embodiments of this disclosure relate to the estimation of nominal stress using stress calculated by finite element (FE).

[0003] This section is intended to introduce the reader to various aspects of the art that may be related to various aspects of the present disclosure, which are described below. It is believed that this discussion will help to provide the reader with background information to facilitate a better understanding of various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this context and not as an admission of prior art.

[0004] Welding fatigue prediction standards generally allow the use of nominal stress metrics. However, the stress in welded structures is typically calculated using FE calculation methods that do not directly calculate the nominal stress. Instead, the nominal stress usually has to be estimated based on, for example, separate calculations. For example, some conventional methods for approximating the nominal stress include using FE - generated forces and moments in combination with manual calculations, while other methods use a coarse FE mesh to minimize the local stress - raising effect at the root of the weld joint, and still other methods extrapolate the FE - calculated stress based on certain geometric parameters such as plate thickness, which may not be readily identifiable in practical applications. Generally, these conventional methods tend to be relatively time - consuming, error - prone, or, in the case of the coarse FE mesh method, somewhat arbitrary or cumbersome. Summary of the Invention

[0005] Certain embodiments commensurate in scope with the originally claimed subject matter are outlined below. These embodiments are not intended to limit the scope of the present disclosure, but rather these embodiments are only intended to provide a brief overview of certain disclosed embodiments. In fact, the present disclosure may cover a variety of forms that may be similar to or different from the embodiments set forth below.

[0006] In one embodiment, a method includes using FE analysis to calculate stresses at multiple points along a baseline of a structural component from a base point. The method further includes identifying two or more of the multiple points having calculated stresses that are determined to be unaffected by a stress elevation effect at the base point. The method further includes estimating a nominal stress at the base point by extrapolating the calculated stresses of two or more of the multiple points to the base point.

[0007] In another embodiment, a method includes using FE analysis to calculate stresses at multiple points along a baseline of a structural component from a base point. The method further includes identifying two or more of the multiple points by evaluating second derivatives of the calculated stresses of adjacent points among the multiple points. The method further includes estimating a nominal stress at the base point by extrapolating the calculated stresses of two or more of the multiple points to the base point.

[0008] In yet another embodiment, a non - transitory computer - readable medium includes instructions for estimating a nominal stress. The instructions are configured to use FE analysis to calculate stresses at multiple points along a baseline of a structural component from a base point. The instructions are further configured to identify two or more of the multiple points by evaluating second derivatives of the calculated stresses of adjacent points among the multiple points. The instructions are further configured to estimate a nominal stress at the base point by extrapolating the calculated stresses of two or more of the multiple points to the base point. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] These and other features, aspects, and advantages of the present disclosure will become better understood when the following detailed description is read with reference to the accompanying drawings, where like characters represent like parts throughout the drawings, and in which: Figure 1 illustrates an embodiment of a control system configured to estimate a nominal stress in a structural component according to an embodiment of the present disclosure; Figure 2 is a perspective view of a welded structural component according to an embodiment of the present disclosure, for which a nominal stress can be estimated by the Figure 1 control system; Figure 3 is a perspective view of a non - welded structural component according to an embodiment of the present disclosure, for which a nominal stress can be estimated by the Figure 1 control system; Figure 4A illustrates a graph of stress values at respective points along a baseline of a structural component such as the Figure 2 and 3 illustrated in the structural component; Figure 4B illustrates an enlarged view of the graph shown in Figure 4A ; Figure 5 is a flowchart of a method for estimating nominal stress in a structural component according to an embodiment of the present disclosure, the method being executable by a Figure 1 control system; and Figure 6 illustrates a graph of spline-fitted stress and a filtered second derivative of stress at various points along a baseline of a structural component such as the Figure 2 and 3 structural component shown in DETAILED DESCRIPTION

[0010] One or more specific embodiments of the present disclosure will be described below. In the process of endeavoring to provide a brief description of these embodiments, not all features of the actual implementation may be described in the specification. It should be understood that in the development of any such actual implementation, as in any engineering or design project, many implementation-specific decisions must be made to achieve the specific goals of the developer, such as in accordance with system-related and business-related constraints, which may vary from implementation to implementation. In addition, it should be understood that such development work may be complex and time-consuming, but still routine tasks of design, fabrication, and manufacture for those of ordinary skill in the art who benefit from the present disclosure.

[0011] When introducing elements of various embodiments of the present disclosure, the articles "a," "an," and "the" are intended to mean that there is one or more elements. The terms "comprising," "including," and "having" are intended to be inclusive and mean that there may be additional elements in addition to the listed elements. Additionally, it should be understood that references to "one embodiment" or "an embodiment" of the present disclosure are not to be construed as excluding the existence of additional embodiments that also incorporate the recited features.

[0012] The embodiments described herein include systems and methods for estimating nominal stress using FE stress calculations without manual calculations, specific mesh density requirements, identifying specific geometric parameters (such as plate thickness), or finite element representations of weld beads. The systems and methods described herein can be used to identify nominal stress in the base material of welded structures and components and also in non-welded components that have stress concentrations for other reasons. The systems and methods described herein also allow for the consistent utilization of readily available FE stress results and provide user feedback regarding the accuracy of the nominal stress approximation. Additionally, the systems and methods described herein are generally faster and less error-prone than the conventional techniques described herein and are relatively insensitive to the mesh density of the FE stress calculations. As used herein, the term "nominal stress" is intended to exclude certain stress concentration effects. Thus, as used herein, it is assumed that the nominal stress along any one baseline exhibits linear behavior at a distance from a base point (such as the root of a weld joint or a stress concentration), where the non-linear effects from the base point are no longer dominant. In certain embodiments, multiple baselines may be employed, and it is assumed that the nominal stress exhibits linear behavior along each baseline. Additionally, in certain embodiments, a linearity check may be performed to verify that the stress exhibits linear characteristics at a distance from the base point.

[0013] Figure 1 An embodiment of a control system 10 configured to estimate nominal stress in a structural component 12 in accordance with an embodiment of the present disclosure is illustrated. As illustrated, in certain embodiments, the control system 10 includes a storage device 14 (e.g., a non-transitory computer-readable medium) and a processor 16 configured to execute computer-readable instructions stored on the storage device 14. In certain embodiments, the processor 16 may include multiple processors, one or more general-purpose microprocessors, one or more special-purpose microprocessors, and / or one or more application-specific integrated circuits (ASICs) or some combination thereof. For example, in certain embodiments, the processor 16 may include one or more reduced instruction set (RISC) processors, advanced RISC machines (ARM) processors, performance-optimized processors with enhanced RISC (PowerPC), field-programmable gate array (FPGA) integrated circuits, graphics processing units (GPU), or any other suitable processing device.

[0014] In some embodiments, the storage device 14 may include volatile memory (such as random access memory (RAM)), non-volatile memory (such as read-only memory (ROM)), flash memory, or any combination thereof. The storage device 14 may store a variety of information that can be used for various purposes. For example, in some embodiments, the storage device 14 may store processor-executable instructions (e.g., firmware or software) for execution by the processor 16, such as instructions for estimating nominal stress in the structural component 12. Additionally, in some embodiments, the processor 16 may store information related to the nominal stress in one or more storage devices 18. For example, in some embodiments, one or more storage devices 18 (e.g., non-volatile storage) may include ROM, flash memory, a hard disk drive, or any other suitable optical, magnetic, or solid-state storage medium, or a combination thereof. Additionally, in some embodiments, the processor 16 may be configured to output a control signal 20 that may be used to control the manufacture of one or more subsequent structural components 12.

[0015] As described in more detail herein, the processor 16 may execute instructions stored in the storage device 14 that relate to using the FE analysis algorithm 22 to calculate the stress at multiple points of the structural component 12. For this purpose, in some embodiments, the processor 16 may utilize one or more models 24 of the structural component 12, which may be stored, for example, in the storage device 14 or one or more storage devices 18 and / or may be received from an information source 26 external to the control system 10. In some embodiments, once the processor 16 has calculated the stress at multiple points of the structural component 12 using the FE analysis algorithm 22, the processor 16 may identify two or more points among the multiple points along the baseline of the structural component 12 (e.g., in a linear direction) that have respective calculated stresses that are not affected by the stress elevation effect at the base point of the structural component 12 (e.g., the root of the weld joint where the welded members of the welded structural component 12 are closest to each other, the stress concentration of the non-welded structural component 12, or some other point where a stress elevation effect may occur). As described in more detail herein, in some embodiments, by, for example, evaluating the second derivative of the calculated stresses of adjacent points among the multiple points of the structural component 12, the processor 16 may identify two or more points along the baseline of the structural component 12 as having respective calculated stresses that are not affected by the stress elevation effect at the base point of the structural component 12.

[0016] It should be noted that in some embodiments, it is not necessary to include the bead geometry in the FE idealization using the FE analysis algorithm 22. Instead, in some embodiments, coincidence nodes or bonded contacts without penetration can be used to idealize the welded joint. Additionally, in some embodiments, the instructions executed by the processor 16 can assume that the stress is only due to external forces and moments; however, in other embodiments, a more complex stress analysis can be performed. It is also noted that in some embodiments, the instructions executed by the processor 16 can assume that the stress at a location far enough from the root of the welded joint or other stress concentration will decrease linearly with the distance from the root of the welded joint, stress concentration, or other point where a stress rise effect may occur; however, again, a more complex stress analysis can be performed in other embodiments. In some embodiments, the processor 16 can perform a linearity check to verify that the stress actually does exhibit linear characteristics at a certain distance from the base point.

[0017] In some embodiments, once the processor 16 has identified two or more points along the baseline of the structural member 12 (the points having corresponding calculated stresses that are not affected by the stress rise effect at the base point of the structural member 12), the processor 16 can estimate the nominal stress at the base point of the structural member 12, for example, by extrapolating the calculated stresses at the two or more identified points back to the base point of the structural member 12. Thus, as described in more detail herein, the processor 16 can estimate the nominal stress at the base point of the structural member 12 with little sensitivity to the mesh density used in the FE analysis algorithm 22. More precisely, the embodiments described herein use a relatively simple extrapolation of the calculated stresses along the baseline of the structural member 12 (e.g., in any linear direction) based on two or more points, the two or more points being determined by the processor 16 to have corresponding calculated stresses that are not affected by the stress rise effect at the base point of the structural member 12.

[0018] The embodiments described herein can be equally applicable to estimating the nominal stress in both welded structural members 12 and non-welded structural members 12. For example, Figure 2 is a perspective view of a welded structural member 12 according to an embodiment of the present disclosure, and the nominal stress for this welded structural member 12 can be estimated by Figure 1 the control system 10 of. As Figure 2As illustrated, the welded structural member 12 includes a base member 28 and an auxiliary member 30 that is welded to the base member 28 via fillet welds 32 on opposite sides of the auxiliary member 30. However, it will be understood that the embodiments described herein can be equally applicable to estimating nominal stresses at other types of welds. As described herein, in certain embodiments, the root of the weld joint (e.g., the intersection between the base member 28 and the auxiliary member 30 for the weld 32) can be considered as a base point 40 at which the nominal stress can be estimated by Figure 1 the control system 10.

[0019] In contrast, Figure 3 is a perspective view of a non-welded structural member 12 according to an embodiment of the present disclosure, for which the nominal stress can be estimated by Figure 1 the control system 10. As Figure 3 illustrated, the non-welded structural member 12 includes a single (e.g., integral) structural member 34. However, as illustrated, Figure 3 the integral structural member 34 of the non-welded structural member 12 includes one or more stress concentration points 36 (e.g., holes or other structural features), at which the nominal stress may be different due to the structural nature of the one or more stress concentration points 36. As described herein, in certain embodiments, Figure 3 one or more stress concentration points 36 of the non-welded structural member 12 illustrated in Figure 1 can be considered as a base point 40 at which the nominal stress can be estimated by

[0020] As Figure 2 and 3 illustrated, regardless of the specific type of the base point (e.g., the weld 32 or the stress concentration point 36), the structural member 12 can be analyzed by Figure 1 the control system 10 (e.g., by the processor 16 executing the FE analysis algorithm 22) to have a certain mesh density to calculate the stress at certain points (e.g., the intersection of the meshes) of the structural member 12. However, as described in more detail herein, the embodiments of the present disclosure are capable of estimating the nominal stress at the base point 40 of the structural member 12 without being significantly affected by the specific mesh density used by the FE analysis algorithm 22. Specifically, also as Figure 2 and 3As illustrated, in some embodiments, once the stress at multiple points of the structural component 12 is calculated using the FE analysis algorithm 22, the processor 16 can consider the FE-calculated stress for each individual point along a straight baseline 38 (e.g., in a linear direction), the straight baseline 38 extending from a base point 40 (e.g., at the root of the weld joint associated with the weld 32 or stress concentration 36) along the baseline 38 to a far point that is a certain linear distance away from the base point 40.

[0021] As described in more detail herein, embodiments of the present disclosure are capable of estimating the nominal stress at the base point 40 of the structural component 12 regardless of the specific geometric features of the structural component 12. More precisely, by considering the FE-calculated stress along a baseline 38 extending from the base point 40 to estimate the nominal stress at the base point 40 of the structural component 12, the embodiments described herein eliminate the need to consider the specific geometric features of the structural component 12 by instead identifying points along the baseline 38 that have calculated stresses determined to be unaffected by the stress elevation effect at the base point 40.

[0022] To further illustrate Figure 1 how the control system 10 estimates the nominal stress at the base point 40 of the structural component 12, Figure 4A a graph is illustrated of the stress values at various points along a baseline 38 of a structural component 12 such as Figure 2 and 3 the structural component 12 illustrated in. In particular, Figure 4A a series 42 of FE-calculated stress values (e.g., as determined by the processor 16 of the control system 10 using the FE analysis algorithm 22) at various positions along the baseline 38 of the structural component 12 is illustrated. It will be understood that a 0 value for the position axis is analogous to the base point 40 of the structural component 12 (e.g., at the root of the weld joint associated with the weld 32 of the welded structural component 12 illustrated in Figure 2 or at the stress concentration 36 of the non-welded structural component 12 illustrated in Figure 3 .

[0023] As Figure 4A illustrated, the processor 16 of the control system 10 can identify two or more points 44 of the series 42 of FE-calculated stress values where the FE-calculated stress values are not affected by the stress elevation effect at the base point 40 of the structural component 12. As illustrated by Figure 4AAs illustrated by line 46 in, once the processor 16 has identified two or more points 44 with stress values from FE calculations that are not affected by the stress elevation effect at the base point 40 of the structural member 12, the processor 16 can extrapolate the stress values from the FE calculations of the two or more points 44 back to a value of 0 on the position axis, which also corresponds to the base point 40 of the structural member 12. The processor 16 of the control system 10 then determines that the intersection point 48 of the extrapolated line 46 with the stress axis is the estimated nominal stress value of the base point 40 of the structural member 12.

[0024] In some embodiments, to identify two or more points 44 with stress values from FE calculations that are not affected by the stress elevation effect at the base point 40 of the structural member 12, the processor 16 of the control system 10 can compare the rate of change (e.g., second derivative) of the slope of a series 42 of stress values from FE calculations of adjacent points along the position axis (e.g., which also corresponds to points along the baseline 38 of the structural member 12). It will be understood that the slope of the calculated stress at any given point along the position axis will be equal to δs / δx at that particular point, and the rate of change (e.g., second derivative) of the slope of the calculated stress at any given point along the position axis will be equal to δ 2 s / δx 2 where s equals the calculated stress (i.e., along the stress axis), and x equals the distance from the base point 40 along the baseline 38 of the structural member 12 (i.e., along the position axis).

[0025] To further illustrate Figure 1 how the control system 10 of Figure 4B identifies two or more points 44 with stress values from FE calculations that are not affected by the stress elevation effect at the base point 40 of the structural member 12, Figure 4A an enlarged view of the graph illustrated in Figure 4B is shown according to an embodiment of the present disclosure. In particular,

[0026] In some embodiments, the processor 16 of the control system 10 may identify the point 62 as one of two or more points 44 having a stress value for FE calculations that is not affected by the stress elevation effect at the base point 40 of the structural member 12. In particular, in some embodiments, the processor 16 of the control system 10 may make this determination based on the fact that a given number of points adjacent to the point 62 have second derivatives that deviate from the second derivative at the point 62 by no more than a threshold percentage. For example, in some embodiments, the processor 16 of the control system 10 may determine that the points 58, 60, 62, 64, and 66 all have second derivatives that deviate from each other by no more than 10%, no more than 5%, no more than 2%, no more than 1%, or less. Accordingly, the processor 16 of the control system 10 may determine that the point 62 is one of two or more points 44 having a stress value for FE calculations that is not affected by the stress elevation effect at the base point 40 of the structural member 12. It will be understood that in such embodiments, the processor 16 of the control system 10 identifies the point 62 as one of two or more points 44 having a stress value for FE calculations that is not affected by the stress elevation effect at the base point 40 of the structural member 12 by analyzing a subset of points adjacent to the point 62 (e.g., the point 62 itself, along with two points on either side of the point 62), such that five points are included in the subset of points. However, it will be understood that in other embodiments, any number of points may be used for the subset of points, such as three points, seven points, nine points, or more.

[0027] Figure 5 is a flowchart of a method 74 for estimating the nominal stress in a structural member 12 according to an embodiment of the present disclosure, and the method 74 may be performed by Figure 1 the control system 10. In particular, as described in more detail herein, Figure 1 the processor 16 of the control system 10 may be configured to execute instructions stored in the storage device 14 of the control system 10, where the instructions are configured to perform Figure 5 the method 74 illustrated in Figure 5 As illustrated in block 76 of Figure 2 in some embodiments, the instructions may include instructions for calculating the stress at a plurality of points extending from a base point 40 (e.g., a weld root associated with a weld 32 of a welded structural member 12 as illustrated in Figure 3 or a stress concentration 36 of a non-welded structural member 12 as illustrated in

[0028] along the baseline 38 of the structural member 12 using the FE analysis algorithm 22. For example, in some embodiments, the processor 16 of the control system 10 may be configured to perform the FE analysis algorithm 22 based on one or more models 24 of the structural member 12 to calculate the stress at a plurality of points along the baseline 38 of the structural member 12.

[0028] Additionally, asFigure 5 As illustrated in block 78, in some embodiments, the instructions may include instructions for identifying two or more points 44 among a plurality of points along a baseline 38 of the structural member 12, the two or more points 44 having stress values from FE calculations determined to be unaffected by the stress elevation effect at the base point 40 of the structural member 12. For example, in some embodiments, the processor 16 of the control system 10 may be configured to identify two or more points 44 having stress values from FE calculations determined to be unaffected by the stress elevation effect at the base point 40 of the structural member 12 by comparing second derivatives of the stress values from FE calculations of adjacent points, e.g., as described in more detail with respect to Figure 4B is described in more detail.

[0029] Additionally, as Figure 5 illustrated in block 80, in some embodiments, the instructions may include instructions for estimating the nominal stress at the base point 40 of the structural member 12 by extrapolating the stress values from FE calculations of the two or more identified points 44 among the plurality of points back to the base point 40 of the structural member 12, e.g., as described in more detail with respect to Figure 4A is described in more detail. As described herein, in some embodiments, the control system 10 may use the estimated nominal stress at the base point 40 of the structural member 12, e.g., to output a control signal (e.g., control signal 20, as Figure 1 illustrated), which may be used to control the manufacture of one or more subsequent structural members 12. For example, in some embodiments, if the processor 16 of the control system 10 estimates the nominal stress at the root of the weld joint associated with the weld 32 of the welded structural member 12 to be higher (or lower) than expected, the processor 16 may output a control signal (e.g., control signal 20, as Figure 1 illustrated) that may be used to adjust the dimensions of the welded structural member 12, adjust the welding process variables, or make any other adjustments for the manufacture of subsequent welded structural members 12.

[0030] In some embodiments, the modeling and simulation performed by the control system 10 may begin by creating a baseline 38 (or a plurality of baselines 38) perpendicular to the weld area of interest. For example, as Figure 2 illustrated, the weld area of interest may include the root of the weld joint associated with the weld 32 (e.g., at the intersection of members 28 30), and the baseline 38 perpendicular to the weld area of interest may include a straight baseline 38 that extends from the base point 40. Generally, the baseline 38 is directly located at the member of interest (i.e., the member that will fail first, e.g., Figure 2onto the base member 28) in the illustrated embodiment. The control system 10 can then create a simulation study for the members 28, 30, one or more loads 82 on the members 28, 30, and the boundary conditions of the members 28, 30 and apply materials. The control system 10 can then model the component contacts that reflect the weld 32, such as the joining contact on the edges of the welded members 28, 30 and the non-penetrating contact between the members 28, 30. The control system 10 can then mesh the structural component 12. In certain embodiments, the control system 10 can apply mesh control (e.g., in combination with a fine mesh option) in the welding region of interest. The control system 10 can then execute the study and ensure that the structural component 12 responds appropriately to the load 82, for example, by considering the displacement deformation results to ensure that the structural component 12 is properly constrained. The control system 10 can then check the von Mises (or other) stress results by probing the baseline 38. In certain embodiments, the control system 10 can ensure that the first nodal value probed resides on the root of the weld joint. Note that when using a metric other than von Mises stress, in certain embodiments, the control system 10 can ensure that the selected metric refers to a coordinate system oriented with respect to the baseline 38. The control system 10 can then extract the stress and position values along the baseline 38.

[0031] Once the stress and position values are extracted by the control system 10, if the position data is not already evenly spaced, the data manipulation performed by the control system 10 can begin by evenly spacing the position data. The control system 10 can then spline fit the stress versus position data (e.g., using a fourth-order spline in certain embodiments). The control system 10 can then take the double difference of the stress with respect to position (e.g., using the central difference method in certain embodiments). The control system 10 can then filter the double-differenced data (e.g., using a Butterworth filter with a low-pass, forward, and backward method having a cutoff frequency of 0.07 and a stop frequency of one in certain embodiments) and plot both the spline-fit stress versus position data and the filtered second derivative of the stress versus position data. Figure 6 illustrates a graph of the spline-fit stress 84 and the filtered second derivative of the stress 86 at various points along the baseline 38 of a structural component 12 such as the structural component 12 illustrated in Figure 2 and 3 in accordance with an embodiment of the present disclosure. The control system 10 can then calculate the absolute difference of the filtered second derivative of the stress 86 between each value of x (e.g., to two decimal places in certain embodiments).

[0032] Then, the control system 10 can identify a first instance along the position (i.e., x) axis where a certain number of consecutive points (e.g., in some embodiments, three consecutive points, five consecutive points, seven consecutive points, nine consecutive points, or more) have an absolute difference of the filtered second derivative of the stress 86 between adjacent points that is less than a given threshold percentage (e.g., in some embodiments, less than 10%, less than 5%, less than 2%, less than 1%, or less). It will be understood that this first identified instance is Figure 4A the first of the identified points 44 illustrated in Figure 4A . In some embodiments, the control system 10 can identify a second point 44 at a certain set distance from the first identified point 44 (e.g., in some embodiments, 1.5 times the position value along the position axis), and the two identified points 44 can be determined to have corresponding calculated stresses that are not affected by the stress-rising effect at the base point 40 of the structural member 12.

[0033] In some embodiments, if the control system 10 determines that the calculated stress associated with the second identified point 44 is greater than a given threshold of the calculated stress associated with the first identified point 44 (e.g., in some embodiments, greater than 10%, greater than 5%, greater than 2%, greater than 1%, or more), then the control system 10 can re-run the analysis only on the data before and including the first identified point 44 along the position axis. In other words, the control system 10 can consider the data beyond the first identified point 44 as exhibiting non-linearity that should be excluded from the analysis. In other cases, the control system 10 can use two (or more) identified points 44 (and, in some embodiments, all the data between these points 44) to perform Figure 4A the linear regression illustrated in Figure 4A . In some embodiments, the control system 10 can ensure that the R-squared value of the linear regression is greater than a given threshold (e.g., in some embodiments, greater than 0.7, greater than 0.75, greater than 0.8, greater than 0.85, greater than 0.9, or more). As described in more detail with respect to Figure 4A Figure 4A , the y-intercept value of the linear regression (i.e., the value of the linearized stress at a position value of 0) represents the estimated nominal stress at the base point 40.

[0034] As described herein, embodiments of the present disclosure provide advantages over conventional systems and methods for determining nominal stress in that: no manual calculations are required; no specific geometry of the structural member 12 is required in the FE representation used by the FE analysis algorithm 22; the mesh density used by the FE analysis algorithm 22 has little effect on the estimated nominal stress; and no identification of specific geometric parameters (such as plate thickness) is required for extrapolation of the nominal stress. Additionally, as described in more detail herein, the nominal stress in a non-welded structural member 12 having a stress concentration 36 due to geometric features, load application, or other features can also be estimated in a manner similar to that of the welded structural member 12.

[0035] Although only certain features of the present disclosure have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the present disclosure. The technology presented and claimed herein is referenced and applied to physical objects and specific examples of a practical nature, which demonstrably improve the art, and are thus not abstract, intangible, or purely theoretical. Further, if any claim appended to the end of this specification contains one or more elements designated as "means for [performing]... [function]" or "step for [performing]... [function]", such elements are intended to be construed in accordance with 35 U.S.C. § 112(f). However, for any claim that contains elements designated in any other manner, such elements are not intended to be construed in accordance with 35 U.S.C. § 112(f).

Claims

1. A welding system, comprising: A welding control system, comprising: A storage medium storing processor-executable instructions including a finite element (FE) analysis algorithm, the finite element analysis algorithm being configured to calculate stresses in a welded structural component and control a welding process of the welding system at least partially based on the calculated stresses ； and One or more processors configured to execute the finite element analysis algorithm, wherein when executed by the one or more processors, the finite element analysis algorithm: Calculates the stresses at a plurality of points along a baseline of the welded structural component from a base point; Identifies two or more of the plurality of points by evaluating second derivatives of the calculated stresses of adjacent points in the plurality of points, wherein identifying the two or more of the plurality of points includes identifying each of the two or more of the plurality of points by identifying a subset of points adjacent to the respective point, and wherein the second derivative of each in the subset of points is within a threshold percentage of each other; Estimates a nominal stress at the base point by extrapolating the calculated stresses of two or more of the identified plurality of points to the base point; Outputs a control signal for adjusting a welding process variable of the welding system at least partially based on the estimated nominal stress at the base point for manufacturing subsequent welded structural components by the welding system; and Starts manufacturing of subsequent welded structural components using the welding system according to the adjusted welding process variables of the welding system.

2. The welding system according to claim 1, wherein when executed by the one or more processors, the FE analysis algorithm spline fits the calculated stresses with the plurality of points along the baseline of the welded structural component from the base point before identifying the two or more points.

3. The welding system according to claim 1, wherein the one or more processors are configured to execute the FE analysis algorithm at least partially based on one or more models of the welded structural component.

4. The welding system according to claim 1, wherein the finite element analysis algorithm does not depend on the bead geometry of the welded structural component.

5. The welding system according to claim 1, wherein the finite element analysis algorithm is not significantly affected by a specific mesh density of the finite element analysis algorithm.

6. The welding system according to claim 1, wherein the welded structural component includes a root of a weld joint at the base point.

7. The welding system according to claim 1, wherein the subset of points includes five points.

8. The welding system according to claim 1, wherein the threshold percentage is 5%.

9. A welding system, comprising: A welding control system, comprising: A storage medium storing processor-executable instructions including a finite element (FE) analysis algorithm, the finite element analysis algorithm being configured to calculate stresses in a welded structural component and control a welding process of the welding system at least partially based on the calculated stresses ； and One or more processors configured to execute the FE analysis algorithm, wherein when executed by the one or more processors, the FE analysis algorithm: Calculate the stress at a plurality of points along the baseline of the welded structural member from a base point; Perform a spline fit of the calculated stress to the plurality of points along the baseline of the welded structural member from the base point; Identify two or more of the plurality of points by evaluating the second derivative of the stress calculated by the spline fit of adjacent points among the plurality of points, wherein identifying the two or more of the plurality of points includes identifying each of the two or more of the plurality of points by identifying a subset of points adjacent to the respective point, and wherein the second derivative of each in the subset of points is within a threshold percentage of each other; Estimate the nominal stress at the base point by extrapolating the calculated stress of the two or more identified points among the plurality of points to the base point; Output a control signal for adjusting a welding process variable of the welding system, at least in part based on the estimated nominal stress at the base point, for manufacturing subsequent welded structural members by the welding system; and Initiate the manufacture of subsequent welded structural members using the welding system according to the adjusted welding process variables of the welding system.

10. The welding system according to claim 9, wherein the one or more processors are configured to perform the finite element analysis algorithm at least in part based on one or more models of the welded structural member.

11. The welding system according to claim 9, wherein the finite element analysis algorithm does not depend on the bead geometry of the welded structural member.

12. The welding system according to claim 9, wherein the finite element analysis algorithm is not significantly affected by a particular mesh density of the finite element analysis algorithm.

13. The welding system according to claim 9, wherein the welded structural member includes a weld joint root at the base point.

14. The welding system according to claim 9, wherein the subset of points includes five points.

15. The welding system according to claim 9, wherein the threshold percentage is 5%.

16. A welding control system, comprising: A storage medium storing processor-executable instructions including a finite element (FE) analysis algorithm configured to calculate the stress of a welded structural member and control the welding process of the welding system at least in part based on the calculated stress ； and One or more processors configured to execute the finite element analysis algorithm, wherein the finite element analysis algorithm, when executed by the one or more processors, causes the welding control system to: Calculate the stress at a plurality of points along the baseline of the welded structural member from a base point; Perform a spline fit of the calculated stress to the plurality of points along the baseline of the welded structural member from the base point; Identifying two or more points among the plurality of points by evaluating second derivatives of stresses calculated by spline fitting of adjacent points among the plurality of points, wherein identifying the two or more points among the plurality of points includes identifying each of the two or more points among the plurality of points by identifying a subset of points adjacent to the respective point, wherein second derivatives of each of the points in the subset of points are within a threshold percentage of each other, wherein the threshold percentage is 5%, and wherein the subset of points includes five points; Estimating a nominal stress at the base point by extrapolating the calculated stresses of the two or more points identified among the plurality of points to the base point; And Outputting a control signal for adjusting a welding process variable of the welding system, at least in part based on the estimated nominal stress at the base point, for fabricating a subsequent welded structural component by the welding system; And Initiating fabrication of a subsequent welded structural component using the welding system according to the adjusted welding process variable of the welding system.

17. The welding control system according to claim 16, wherein the one or more processors are configured to perform the finite element analysis algorithm at least in part based on one or more models of the welded structural component.

18. The welding control system according to claim 16, wherein the finite element analysis algorithm does not depend on the bead geometry of the welded structural component.

19. The welding control system according to claim 16, wherein the finite element analysis algorithm is not significantly affected by a particular mesh density of the finite element analysis algorithm.

20. The welding control system according to claim 16, wherein the welded structural component includes a weld joint root at the base point.

21. A welding system, comprising: A welding control system, comprising: A storage medium storing processor-executable instructions including a finite element (FE) analysis algorithm configured to calculate stresses of a welded structural component and control a welding process variable of the welding system at least in part based on the calculated stresses; and One or more processors configured to execute the finite element analysis algorithm, wherein, when the FE analysis algorithm is executed by the one or more processors: Calculating stresses at a plurality of points along a baseline of the welded structural component from a base point; Identifying two or more points among the plurality of points by evaluating second derivatives of the calculated stresses of adjacent points among the plurality of points; Estimating a nominal stress at the base point by extrapolating the calculated stresses of the two or more points identified among the plurality of points to the base point; Adjusting a welding process variable of the welding system at least in part based on the estimated nominal stress at the base point; Initiating fabrication of a subsequent welded structural component using the welding system according to the adjusted welding process variable of the welding system.

22. The welding system according to claim 21, wherein identifying the two or more points among the plurality of points includes identifying each of the two or more points among the plurality of points by identifying a subset of points adjacent to the respective point.

23. The welding system according to claim 22, wherein the subset of points includes at least five points.

24. The welding system according to claim 22, wherein the second derivative of each point in the subset of points is within a threshold percentage of each other.

25. The welding system according to claim 24, wherein the threshold percentage is less than 5%.

26. The welding system according to claim 21, wherein when the finite element analysis algorithm is executed by the one or more processors, before identifying the two or more points, a spline fit is performed on the calculated stress and the plurality of points along the baseline of the welded structural member from the base point.

27. The welding system according to claim 21, wherein the one or more processors are configured to execute the finite element analysis algorithm at least in part based on one or more models of the welded structural member.

28. The welding system according to claim 21, wherein the welded structural member includes a weld root at the base point.

29. A welding control system comprising: a storage medium storing processor-executable instructions including a finite element (FE) analysis algorithm configured to calculate the stress of a welded structural member and control welding process variables of the welding system at least in part based on the calculated stress; and one or more processors configured to execute the finite element analysis algorithm, wherein when the finite element analysis algorithm is executed by the one or more processors: calculate the stress at a plurality of points along the baseline of the welded structural member from the base point; perform a spline fit on the calculated stress and the plurality of points along the baseline of the welded structural member from the base point; identify two or more points among the plurality of points by evaluating the second derivative of the calculated stress of the spline fit for adjacent points among the plurality of points; estimate the nominal stress at the base point by extrapolating the calculated stress of the two or more points identified among the plurality of points to the base point; regulate the welding process variables of the welding system at least in part based on the estimated nominal stress at the base point; initiate the manufacture of subsequent welded structural members using the welding system according to the regulated welding process variables of the welding system.

30. The welding control system according to claim 29, wherein identifying the two or more points among the plurality of points includes identifying each of the two or more points among the plurality of points by identifying a subset of points adjacent to the respective point.

31. The welding control system according to claim 30, wherein the subset of points includes at least five points.

32. The welding control system according to claim 30, wherein the second derivative of each point in the subset of points is within a threshold percentage of each other.

33. The welding control system according to claim 32, wherein the threshold percentage is less than 5%.

34. The welding control system according to claim 29, wherein the one or more processors are configured to perform the FE analysis algorithm at least in part based on one or more models of the welded structural component.

35. The welding control system according to claim 29, wherein the welded structural component includes a root of a weld joint at the base point.

36. A welding control system comprising: a storage medium storing processor-executable instructions including a finite element (FE) analysis algorithm configured to calculate stresses in a welded structural component and control welding process variables of a welding system at least in part based on the calculated stresses; one or more processors configured to execute the finite element analysis algorithm, wherein when the finite element analysis algorithm is executed by the one or more processors: calculate stresses at a plurality of points along a baseline of the welded structural component from a base point; identify two or more of the plurality of points by evaluating second derivatives of the calculated stresses of adjacent points among the plurality of points; estimate a nominal stress at the base point by extrapolating the calculated stresses of two or more of the identified plurality of points to the base point; regulate the welding process variables of the welding system at least in part based on the estimated nominal stress at the base point; initiate fabrication of a subsequent welded structural component using the welding system according to the regulated welding process variables of the welding system.

37. The welding control system according to claim 36, wherein identifying the two or more of the plurality of points includes identifying each of the two or more of the plurality of points by identifying a subset of points adjacent to the respective point.

38. The welding control system according to claim 37, wherein second derivatives of each point in the subset of points are within a threshold percentage of each other.

39. The welding control system according to claim 36, wherein when the finite element analysis algorithm is executed by the one or more processors, the calculated stresses are spline-fitted to the plurality of points along the baseline of the welded structural component from the base point before identifying the two or more points.

40. The welding control system according to claim 36, wherein the one or more processors are configured to perform the finite element analysis algorithm at least in part based on one or more models of the welded structural component.

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