User unit techniques for implementing color model / high fixtiality computer-assisted

Abstract

A method of modeling a joint by analytically eliminating a series of internal degrees of freedom for representing an actual weld or joint stiffness in a structure using User Unit (UEL) technology. The obtained formula is in a closed form, and calculation accuracy and simplicity of structure application can be achieved. For point joints, a detailed annular finite element required to achieve reasonable accuracy may be replaced by a simple finite element mesh using only four user elements. The UEL joint modeling method provides an accurate stress calculation result compared to a grid insensitive structural stress method and detailed explicit joint representation of the joint. The UEL method may also be applied to modeling seam welded joints, such as MIG, laser, and friction stir welding. Without losing any accuracy, the UEL panel / shell unit does not require explicit representation of weld fillet geometry required by existing methods.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Patent Application No. 18 / 175,756, filed on February 28, 2023, and also claims the benefit of U.S. Provisional Application No. 63 / 315,189, filed on March 1, 2022. The entire disclosure of the above application is incorporated herein by reference. Technical Field

[0003] The present disclosure relates to spot joint (or welded, including seam welded) structures, and more particularly, to user unit technology for implementing coarse model / high fidelity Computer-Aided Engineering (CAE) durability assessment of such structures.

[0004] Background and Summary of the Invention

[0005] This section provides background information related to the present disclosure which is not necessarily prior art. This section provides a general overview of the present disclosure and is not a comprehensive disclosure of its full scope or all of its features.

[0006] In most vehicle structures, there are thousands of spot welds or other types of joints (including mechanical fastening (e.g., self-piercing rivet guns), laser or arc welds, or seam joints). These joints are severe stress concentrators, susceptible to fatigue damage under time-varying operating loads, and pose a major challenge to new vehicle development. In today's competitive environment, durability testing at the component and vehicle level is time-consuming and costly.

[0007] To ensure structural durability in rapid prototyping, reliable joint modeling methods become critical to determine joint locations / spacings during the design phase and to minimize the physical testing required to ensure vehicle durability (commonly referred to as Computer Aided Engineering (CAE) or CAE durability simulation or modeling).

[0008] Currently, existing CAE modeling techniques with commercial finite element (FE) packages (even when using the most advanced methods to date) either suffer from mesh size and mesh type sensitivity in the stress calculations around joints or require an explicit representation of the joint geometry. Available joint modeling scenarios are either too complex and time-consuming to be used for complex structures (e.g., a typical passenger car contains thousands of point joints and a commercial vehicle cab structure contains approximately 7,000 point joints) or too simplistic to produce reliable results. As a result, the uncertainties inherent in simplistic joint modeling approaches require exhaustive testing at all stages of vehicle development, often resulting in the use of many more joints than are actually necessary.

[0009] Therefore, according to the principles of the present teachings, a method for modeling joints using "User Element" (UEL) technology is provided. In the case of modeling point joints, the "User Element" (UEL) modeling of the present teachings has been developed by eliminating a series of internal degrees of freedom representing the actual weld or joint stiffness in the structure through rigorous analytical formulas. Thus, for example, a detailed annular finite element can be replaced by a simple finite element mesh using only four user elements to represent the point joint. For a typical body-in-white structure containing many point connections, the use of UEL can save at least 10 times the modeling generation cost. In addition to significantly simplifying the modeling requirements, the UEL joint modeling method also provides accurate stress calculation results compared to the methods used today through mesh-insensitive structural stress methods and detailed explicit joint representation of the joints compared to the methods used today.

[0010] In the case of modeling butt weld joints, the UEL method of the present teaching can also be applied to model butt weld joints such as inert gas welding (MIG), laser welding, and friction stir welding. The explicit representation of the weld fillet geometry can be represented by simple UEL plate / shell elements.

[0011] Further areas of applicability will become apparent from the description provided herein.The description and specific examples in this summary are intended for illustrative purposes only and are not intended to limit the scope of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.

[0013] Figure 1 is a schematic representation of point joints formed by four "user units" (UELs) on each of two sheets in accordance with the principles of the present disclosure;

[0014] Figures 2A and 2B are examples of VERITY 3D images available in commercial durability software. TM Schematic diagram of the existing explicit point joint modeling technique for the method. Note that other available methods that use the joint representation shown but without conventional elements cannot produce credible stress results, for example, the LBF method;

[0015] Figure 3 is a comparison of a conventional 36×36K matrix of virtual nodes and a 24×24K matrix of virtual nodes simplified by analysis with imposed point joint constraints using the existing explicit point joint modeling technique of the present invention for coarse grid / high fidelity computer aided design durability assessment in accordance with the principles of the present disclosure;

[0016] Figure 4 is based on the principles of the present disclosure by applying membrane joint constraints 7-1, 7-2, 7-5 K m Illustration of virtual nodes 1, 2, and 5 of the matrix;

[0017] Figure 5 It is a schematic diagram of implementing UEL in finite element software;

[0018] Figure 6 is an example ABAQUS according to the principles of the present disclosure TM Graphic illustration of the user subroutine interface;

[0019] FIG. 7A is a diagram including a method according to existing direct methods (eg, VERITY TM ) is an illustration of a component with two spot welds modeled;

[0020] Figure 7B is an illustration of a component containing two spot welds modeled according to the UEL method;

[0021] Figure 8 is a first comparative graph of stress per unit load versus angle (degrees) around a spot weld edge according to a direct stress test method, a UEL method according to the principles of the present disclosure, and a conventional "LBF" method used in various commercial structural durability software packages (which also allows for a simple joint representation, but lacks the desired accuracy);

[0022] FIG. 9A is a graph obtained by a direct method (eg, ABAQUS TM ) Illustration of a component containing two point joints under lap shear loading;

[0023] Fig. 9B is a diagram of a component with two point joints in a lap shear specimen according to the UEL method;

[0024] Fig.10is a second comparison graph of stress concentration factor (SCF) versus angle (degrees) for lap shear specimens according to a direct stress test method, a UEL method according to principles of the present disclosure, and a conventional "LBF" method used in commercial structural durability software packages;

[0025] Fig.11A (Left) is a schematic three-dimensional (3D) representation of a seam welded component using UEL from existing explicit welding modeling techniques, where 3D fillet welds (with triangular cross-sections) exist in today's structural durability simulation software; Fig.11A (Right) is a schematic representation of the same 3D part using UEL, where only plate or shell elements are required without any loss of accuracy;

[0026] Fig. 11B (Left) is a representation of a finite element model using solid elements with explicit fillet weld representation; Fig. 11B (Right) is a representation of the finite element model using UEL to achieve the same computational accuracy for a simple representation of a fillet weld.

[0027] Fig.12 is a schematic diagram of an existing explicit T-joint seam weld modeling technique for representing an actual 3D plate fillet weld component in a structure;

[0028] Fig.13 (Left) is a schematic representation of a finite element model using solid elements with explicit fillet weld representation. Fig.13 (Right) is a schematic representation of T-joint seam weld modeling using UEL, where not only does it not require modeling of 3D fillet welds, but only simple shell or plate elements are required;

[0029] Fig.14A is an illustration of the actual nodes (5 and 6) of the conventional seam weld joint modeling technique with two plate elements in existing structural durability software;

[0030] Fig. 14B How to eliminate the joint membrane in UEL by applying seam joint constraints on two virtual nodes in the UEL formula according to the principles of the present disclosure Fig.14A Illustration of two actual nodes in ;

[0031] Fig.15A is a diagram of a lap fillet weld joint according to the UEL method;

[0032] FIG15B is an illustration of a lap fillet weld joint according to a conventional method;

[0033] Fig.16A is a two-element representation of a T-shaped fillet weld according to the UEL method. Fig.13 Side view of B;

[0034] FIG. 16B is a three-element representation of a T-shaped fillet weld according to a conventional method. Fig.13 Side view of A;

[0035] Fig.17 is a diagram of a 4-node element of arbitrary shape used to represent points in complex structures according to the UEL method;

[0036] Fig.18 is a bar graph comparing stress concentration factors (SCFs) of T-shaped fillet welds according to a conventional method and according to a UEL method in accordance with the principles of the present disclosure;

[0037] Fig.19 is a validation bar graph of maximum stresses of a T-shaped fillet weld component calculated according to a conventional method, according to a coarse model using a UEL method according to the principles of the present disclosure, and without using a UEL method;

[0038] Fig. 20 A coordinate diagram showing the predictability of fatigue life using structural stress range (megapascals (MPa)) versus life (cycles) using coarse mesh finite element modeling based on UEL;

[0039] Fig.21 It is a coordinate diagram of the conventional modeling method using nominal stress range (Mpa) versus life (cycles) to show the predictability of fatigue life;

[0040] Fig. 22 is a graph of UEL coarse mesh finite element modeling using structural stress range (Mpa) versus life (cycles) to demonstrate the predictability of fatigue life in welds of different materials (e.g., aluminum to steel); and

[0041] Fig.23 It is a coordinate diagram of the conventional modeling approach using structural stress range (Mpa) versus life (cycles) to demonstrate the predictability of fatigue life in welds of different materials (e.g., aluminum to steel).

[0042] Corresponding reference characters indicate corresponding parts throughout the several views of the drawings. DETAILED DESCRIPTION

[0043] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0044] Each example embodiment is provided so that the present disclosure will be thorough and the scope will be fully conveyed to those skilled in the art. Many specific details (such as examples of specific components, devices and methods) are set forth to provide a thorough understanding of the embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be used, and each example embodiment can be embodied in many different forms, and neither should be construed as limiting the scope of the present disclosure. In some example embodiments, known processes, known device structures, and known technologies are not described in detail.

[0045] The terms used herein are only used for the purpose of describing specific example embodiments and are not intended to be limiting. Unless the context clearly indicates otherwise, as used herein, the singular forms "one", "an" and "the" may also be intended to include plural forms. The terms "include", "comprise", and "have" are inclusive and therefore specify the presence of the features, unity, steps, operations, units and / or parts, but do not exclude the presence or addition of one or more other features, unity, steps, operations, units, parts and / or combinations thereof. Unless the order of execution is specifically specified, the method steps, processes and operations described herein should not be interpreted as necessarily requiring them to be performed in the specific order discussed or illustrated. It should also be understood that additional or alternative steps may be adopted.

[0046] Although the terms first, second, third, etc. can be used herein to describe various units, components, regions, layers and / or parts, these units, components, regions, layers and / or parts should not be limited by these terms. These terms can only be used to distinguish a unit, component, region, layer or part from another region, layer or part. Terms such as "first", "second" and other numerical terms used in this article do not imply sequence or order unless the context clearly indicates. Therefore, without departing from the teaching of this example embodiment, the first unit, component, region, layer or part discussed below can be referred to as the second unit, component, region, layer or part.

[0047] 1. Point joint modeling

[0048] Through rigorous formulation, "User Elements" (UEL) have been developed by eliminating a series of internal degrees of freedom at virtual nodes that represent actual welds or joint stiffness in the body structure. The welds being modeled can be welds connecting components such as, but not limited to, front rails, side rails, rear rails, floor members, firewall members, floor cross members, roof cross members, A-pillars, B-pillars, and other body parts. The resulting UEL joint representation in the complex structure becomes Figure 1 or Fig.11A (right) or Fig.13As simple as shown in B, where a simplified UEL connector is connected between the two boards.

[0049] 2A and 2B are examples of point joints modeled using existing explicit point joint modeling techniques in commercially available structural durability software (e.g., VERITY 3D for point joints between two plates). TM ) are two illustrations of the point joint representation (FIG. 2A shows a top plate view, while FIG. 2B is a cross-sectional view of section AA as shown in FIG. 2A).

[0050] Figure 3 Schematic diagram of the UEL developed to model a quarter spot weld. The actual nodes 1, 2, and 5 in the conventional 36×36K matrix of the existing explicit spot joint modeling technique using the coarse grid / high-fidelity computer-aided design durability assessment of the present invention are replaced with virtual nodes (left), so that the internal degrees of freedom at the virtual nodes can be eliminated and analytically simplified to a 24×24K matrix (right) by applying the spot joint constraints shown in dashed lines according to the principles of the present disclosure.

[0051] refer to Figure 3 and Figure 4 The analytical process for generating the UEL formulation will now be described. The UEL formulation includes point joint constraints at virtual nodes (1, 2, and 5). Shell / plate elements in commercial finite element codes such as ABAQUS include membrane K m And board K b The element stiffness (K) matrix is ​​a combination of the element stiffness (K) matrix. The membrane element has two degrees of freedom at each node, namely u, v, where u, v and w represent the displacements in the X, Y and Z directions. The plate bending element has three degrees of freedom at each node, namely w, θx, θy, where θx, θy represent the rotations in the X and Y directions. The coordinates of nodes 1, 2, 3 and 4 in this example are:

[0052] Node 1: (x1, y1) = (0, a)

[0053] Node 2:

[0054] Node 3: (x3,y3) = (b,b)

[0055] Node 4: (x4,y4) = (0,b)

[0056] Where a = joint weld nugget radius, and b = element size.

[0057] The UEL formulation also includes the imposition of membrane joint constraints in the equations:

[0058] K m U=F (1)

[0059]

[0060] Among them, u i , v i is the displacement along the X and Y directions at node i, and F xi , F yi is the force in the X and Y directions at node i.

[0061] The applied membrane connector constraints include rigid motion relations:

[0062] u1=u2=u5=u7

[0063] v1=v2=v5=v7

[0064] And the force balance equation:

[0065] F x7 =F x1 +F x2 +F x5 (3)

[0066] F y7 =F y1 +F y2 +F y5 (4)

[0067] The UEL formula makes K m is a 12×12 matrix. For numerical stability, an additional drilling degree of freedom θ is added z .

[0068] By applying a membrane joint constraint, the UEL formulation provides the first part of two shell elements (e.g., "S4" in ABAQUS).

[0069] The displacement vector is expressed as:

[0070]

[0071] Then, for the first S4 shell element:

[0072]

[0073] For the second S4 shell element:

[0074]

[0075] The above calculations for the stiffness matrix components result in the following formulation:

[0076] K 11 u1+K 12 v1+K 13 u2+K 14 v2+K15 u3+K 16 v3+K 17 u4+K 18 v4+K 19 u5+K 1，10 v5+K 1，11 u6+K 1，12 v6=F x1 (8)

[0077] K 21 u1+K 22 v1+K 23 u2+K 24 v2+K 25 u3+K 26 v3+K 27 u4+K 28 v4+K 29 u5+K 2，10 v5+K 2，11 u6+K 2，12 v6=F y1 (9)

[0078] K 31 u1+K 32 v1+K 33 u2+K 34 v2+K 35 u3+K 36 v3+K 37 u4+K 38 v4+K 39 u5+K 3，10 v5+K 3，11 u6+K 3，12 v6=F x2 (10)

[0079] K 41 u1+K 42 v1+K 43 u2+K 44 v2+K 45 u3+K 46 v3+K 47 u4+K 48 v4+K 49 u5+K 4，10 v5+K 4，11 u6+K 4，12 v6=F y2 (11)

[0080] K 51 u1+K 52 v1+K 53 u2+K 54 v2+K 55u3+K 56 v3+K 57 u4+K 58 v4+K 59 u5+K 5，10 v5+K 5，11 u6+K 5，12 v6=F x3 (12)

[0081] K 61 u1+K 62 v1+K 63 u2+K 64 v2+K 65 u3+K 66 v3+K 67 u4+K 68 v4+K 69 u5+K 6，10 v5+K 6，11 u6+K 6，12 v6=F y3 (13)

[0082] K 71 u1+K 72 v1+K 73 u2+K 74 v2+K 75 u3+K 76 v3+K 77 u4+K 78 v4+K 79 u5+K 7，10 v5+K 7，11 u6+K 7，12 v6=F x4 (14)

[0083] K 81 u1+K 82 v1+K 83 u2+K 84 v2+K 85 u3+K 86 v3+K 87 u4+K 88 v4+K 89 u5+K 8，10 v5+K 8，11 u6+K 8，12 v6=F y4 (15)

[0084] K 91 u1+K 92 v1+K 93 u2+K 94 v2+K 95 u3+K96 v3+K 97 u4+K 98 v4+K 99 u5+K 9，10 v5+K 9，11 u6+K 9，12 v6=F x5 (16)

[0085] K 10，1 u1+K 10，2 v1+K 10，3 u2+K 10，4 v2+K 10，5 u3+K 10，6 v3+K 10，7 u4+K 10，8 v4+K 10，9 u5+K 10，10 v5+K 10， 11 u6+K 10，12 v6=F y5 (17)

[0086] K 11，1 u1+K 11，2 v1+K 11，3 u2+K 11，4 v2+K 11，5 u3+K 11，6 v3+K 11，7 u4+K 11，8 v4+K 11，9 u5+K 11，10 v5+K 11， 11 u6+K 11，12 v6=F x6 (18)

[0087] K 12，1 u1+K 12，2 v1+K 12，3 u2+K 12，4 v2+K 12，5 u3+K 12，6 v3+K 12，7 u4+K 12，8 v4+K 12，9 u5+K 12，10 v5+K 12， 11 u6+K 12，12 v6=F y6 (19)

[0088] The above equations are combined with the rigid motion equations u1=u2=u5=u7 and v1=v2=v5=v7 to obtain the following joint membrane constraint equations:

[0089] (K 11 +K 13 +K 19 )u7+(K 12 +K 14 +K 1，10 )v7+K 15 u3+K 16 v3+K 17 u4+K 18 v4+K 1，11 u6+K 1，12 v6=F x1 (20)

[0090] (K 21 +K 23 +K 29 )u7+(K 22 +K 24 +K 2,10 )v7+K 25 u3+K 26 v3+K 27 u4+K 28 v4+K 2,11 u6+K 2，12 v6=F y1 (21)

[0091] (K 31 +K 33 +K 39 )u7+(K 32 +K 34 +K 3，10 )v7+K 35 u3+K 36 v3+K 37 u4+K 38 v4+K 3，11 u6+K 3，12 v6=F x2 (22)

[0092] (K 41 +K 43 +K 49 )u7+(K 42 +K 44 +K 4,10 )v7+K 45 u3+K 46 v3+K 47 u4+K 48 v4+K 4,11 u6+K 4,12 v6=F y2 (23)

[0093] (K 51 +K 53 +K 59 )u7+(K 52 +K 54 +K 5，10 )v7+K 55 u3+K 56 v3+K 57 u4+K 58 v4+K 5，11 u6+K 5，12 v6=F x3 (24)

[0094] (K 61 +K 63 +K 69 )u7+(K 62 +K 64 +K 6,10 )v7+K 65 u3+K 66 v3+K 67 u4+K 68 v4+K 6,11 u6+K 6,12 v6=F y3 (25)

[0095] (K 71 +K 73 +K 79 )u7+(K 72 +K 74 +K 7,10 )v7+K 75 u3+K 76 v3+K 77 u4+K 78 v4+K 7,11 u6+K 7,12 v6=F x4 (26)

[0096] (K 81 +K 83 +K 89 )u7+(K 82 +K 84 +K 8,10 )v7+K 85 u3+K 86 v3+K 87 u4+K 88 v4+K 8,11 u6+K 8,12 v6=F y4 (27)

[0097] (K 91 +K93 +K 99 )u7+(K 92 +K 94 +K 9,10 )v7+K 95 u3+K 96 v3+K 97 u4+K 98 v4+K 9,11 u6+K 9,12 v6 = F x5 (28)

[0098] (K 10，1 +K 10，3 +K 10，9 )u7+(K 10，2 +K 10，4 +K 10，10 )v7+K 10，5 u3+K 10，6 v3+K 10，7 u4+K 10，8 v4+K 10，11 u6+K 10，12 v6 = F y5 (29)

[0099] (K 11，1 +K 11，3 +K 11，9 )u7+(K 11，2 +K 11，4 +K 11，10 )v7+K 11，5 u3+K 11，6 v3+K 11，7 u4+K 11，8 v4+K 11，11 u6+K 11，12 v6 = F x6 (30)

[0100] (K 12，1 +K 12，3 +K 12，9 )u7+(K 12，2 +K 12，4 +K 12，10 )v7+K 12，5 u3+K 12，6 v3+K 12，7 u4+K 12，8 v4+K 12，11 u6+K 12，12 v6 = F y6 (31)

[0101] Apply the force balance equation,

[0102] Fx7 =F x1 +F x2 +F x5 (32)

[0103] F y7 =F y1 +F y2 +F y5 (33)

[0104] The following joint membrane constraint equation is obtained:

[0105] (20)+(22)+(28): (34)

[0106] (K 11 +K 13 +K 19 +K 31 +K 33 +K 39 +K 91 +K 93 +K 99 )u7+(K 12 +K 14 +K 1，10 +K 32 +K 34 +K 3，10 +K 92 +K 94 +K 9，10 )v7+(K 15 +K 35 +K 95 )u3+(K 16 +K 36 +K 96 )v3+(K 17 +K 37 +K 97 )u4+(K 18 +K 38 +K 98 )v4+(K 1，11 +K 3，11 +K 9，11 )u6+(K 1，12 +K 3，12 +K 9，12 )v6=F x7 (35)

[0107] (21)+(23)+(29): (36)

[0108] (K 21 +K 23 +K 29 +K 41 +K 43+K 49 +K 10，1 +K 10，3 +K 10，9 )u7+(K 22 +K 24 +K 2，10 +K 42 +K 44 +K 4，10 +K 10，2 +K 10，4 +K 10，10 )v7+(K 25 +K 45 +K 10，5 )u3+(K 26 +K 46 +K 10，6 )v3+(K 27 +K 47 +K 10，7 )u4+(K 28 +K 48 +K 10，8 )v4+(K 2，11 +K 4，11 +K 10，11 )u6+(K 2，12 +K 4，12 +K 10，12 )v6=F y7 (37)

[0109] (K 11，1 +K 11，3 +K 11，9 )u7+(K 11，2 +K 11，4 +K 11，10 )v7+K 11，5 u3+K 11，6 v3+K 11，7 u4+K 11，8 v4+K 11,11 u6+K 11，12 v6=F x6 (38)

[0110] (K 12，1 +K 12，3 +K 12，9 )u7+(K 12，2 +K 12，4 +K 12，10 )v7+K 12，5 u3+K 12，6 v3+K 12，7 u4+K 12，8 v4+K 12,11 u6+K 12，12 v6=F y6(39)

[0111] (K 51 +K 53 +K 59 )u7+(K 52 +K 54 +K 5，10 )v7+K 55 u3+K 56 v3+K 57 u4+K 58 v4+K 5，11 u6+K 5，12 v6=F x3 (40)

[0112] (K 61 +K 63 +K 69 )u7+(K 62 +K 64 +K 6，10 )v7+K 65 u3+K 66 v3+K 67 u4+K 68 v4+K 6，11 u6+K 6，12 v6=F y3 (41)

[0113] (K 71 +K 73 +K 79 )u7+(K 72 +K 74 +K 7，10 )v7+K 75 u3+K 76 v3+K 77 u4+K 78 v4+K 7，11 u6+K 7，12 v6=F x4 (42)

[0114] (K 81 +K 83 +K 89 )u7+(K 82 +K 84 +K 8，10 )v7+K 85 u3+K 86 v3+K 87 u4+K 88 v4+K 8，11 u6+K 8，12 v6=F y4 (43)

[0115] supply

[0116] The final membrane stiffness matrix K without drilling degrees of freedom m The UEL formula for (8×8) is expressed in closed form as:

[0117] Where i, j = 1, 2, .. 8, for example,

[0118]

[0119] The complete expression for this equation is as follows:

[0120]

[0121] Where a = joint / weld size, b = square element size, E = material Young's modulus, v = Poisson's ratio, t = thickness of the metal sheet. This example equation is based on square elements around the joint / point and is displayed analytically using the software MAPLE for demonstration purposes. The developed UEL can be used for elements of any shape and the numerical method is used to perform the calculation in UEL. Calculation.

[0122] The UEL formulation involves imposing joint bending constraints in the following equations:

[0123] K b d=F (46)

[0124]

[0125] Rigid equations of motion / constraints include:

[0126]

[0127] where w i = displacement of node i along the Z direction.

[0128] θ xi ,θ yi = The rotation along the X and Y directions at node i.

[0129] The force / torque balance equations / constraints include:

[0130] F z7 =F z1 +F z2 +F z5 (53)

[0131]

[0132] where Fzi = force in the Z direction at node i, and

[0133] Mxi, Myi = moments at node i in the X and Y directions.

[0134] This produces K b :18×18.

[0135] The joint bending constraint equation is expressed as follows:

[0136]

[0137]

[0138] The rigid motion equation is:

[0139]

[0140]

[0141] Using the force / torque balance equation:

[0142] F z7 =F z1 +F z2 +F z5 (83)

[0143]

[0144]

[0145]

[0146] K b Simplified to 12×12.

[0147] It can be obtained from major commercial finite element software vendors (such as ABAQUS TM ) provides a user interface that directly uses the final results of the UEL method. For demonstration purposes, for example, the UEL technique is used in ABAQUS TM The implementation in is as Figure 5 and Figure 6 The user unit subroutine (UEL) in

[0148] U = displacement,

[0149] AMATRX = UEL stiffness matrix, and

[0150] RHS = force / torque vector.

[0151] Therefore, any user of a commercial FE package, once they have gained access to the UEL subroutines, can treat UEL as a regular element in their element library for use in performing their own Computer Aided Engineering (CAE) structural analysis. Perform UEL model calculations and use UEL data in commercial finite element packages. Specifically, fill all 24×24 entries of the UEL stiffness matrix K into the array "AMTRX" on the left, such as k(1,1) above. The verified UEL Fortran code is compatible with ABAQUS TM Interactive for large numbers of spot welded parts.

[0152] The stresses around the joints that are critical for structural durability or fatigue assessment can then be calculated by invoking two well documented methods using nodal forces and nodal moments at virtual nodes inside the UEL element. The two methods for calculating structural stresses at joints with demonstrated mesh size insensitivity include:

[0153] Method 1: Decompose the nodal forces / moments into a series of simple load patterns that can be solved analytically, and then add them to the total structural stress solution (see Zhang, Lunyu, Pingsha Dong, Yuedong Wang, and Jifa Mei, "A Coarse-Mesh hybrid structural stress method for fatigue evaluation of Spot-Welded structures." International Journal of Fatigue 164 (2022): 107109).

[0154] Method 2: Apply the simultaneous equations method (see Zhang et al., 2022) by converting the nodal forces / moments about the virtual nodes into linear forces / moments. The structural stress around the joint can be calculated by dividing the linear force by the plate thickness and the linear moment by the plate section modulus.

[0155] As shown in Figure 7A and Figure 7B As shown, the effectiveness and simplicity of the UEL model approach have been demonstrated by a large number of spot welded components under various loading conditions. Figure 7A is an illustration of a two-point joint according to the direct method. Figure 7B is a diagram of a two-point joint modeled according to the UEL method. Figure 8The first comparison plot of stress per unit load versus angle (degrees) according to the direct stress test method, the UEL method according to the principles of the present disclosure, and the conventional "LBF" method used in commercial computer-aided engineering software. The correct solution (labeled "direct method") using a rather complex joint representation scheme was obtained by a state-of-the-art mesh-insensitive method ("The master SN curve method an implementation for fatigue evaluation of welded components" in Section 8, Part 2 of the ASME B&PV Code and API 579-1 / ASME FFS-1 by Dong, P., J. K. Hong, D. A. Osage, D. J. Dewees, and M. Prager. Welding Research Council Bulletin No. 523, 2010), which is not suitable for modeling a large number of point joints in complex structures. In all cases, the solutions using the UEL technique did not deviate significantly from the reference solution. All other solution techniques in the literature and commercial finite element programs failed to provide reasonable solutions.

[0156] As another verification technique, FIG. 9A is an illustration of two point joints in a lap shear specimen according to the direct method. Fig. 9B is a graphic representation of two point joints in a lap shear specimen according to the UEL method. Fig.10 is a second comparison of the stress concentration factor (SCF) versus angle (degrees) for lap shear specimens according to the direct stress test method, the UEL method according to the principles of the present disclosure, and the conventional "LBF" method used in commercial computer-aided engineering software. Again, in all cases, the solution using the UEL technique does not deviate significantly from the reference "direct method" solution.

[0157] 2. Seam welding joint modeling

[0158] The above-mentioned UEL technique can be applied to model seam joints, such as seam joints formed by fusion welding processes (e.g., laser beam welding (LBW), metal inert gas (MIG)) or other solid-state welding processes (e.g., friction-based welding or bonding, including friction stir welding (FSW), etc.). Fig.11A and Fig. 11B is a schematic representation of the development of a seam weld model using UEL from existing explicit parallel seam weld joint modeling techniques using a coarse mesh / high fidelity CAD durability assessment of automotive structures. Similarly, Fig.12is a schematic diagram of the existing explicit T-joint seam weld modeling technique for durability assessment using a coarse mesh / high fidelity computer-aided design of automotive structures, and Fig.13 A and Fig.13 B is a schematic representation of modeling a T-joint seam weld using explicit fillet weld representation and using UEL, respectively. Figure 14 is an illustration of virtual nodes of a conventional seam weld joint modeling technique with seam joint membrane constraints applied to provide virtual nodes of UEL nodes in accordance with the principles of the present disclosure.

[0159] The decomposition of the shell element stiffness matrix is ​​as follows;

[0160]

[0161] The membrane unit is represented by the following formula:

[0162]

[0163] And the plate element is represented by:

[0164]

[0165] Applying seam joint membrane constraints requires assembling two membrane element stiffness matrices and applying constraints including the following rigid kinematic relations:

[0166] U x5 =U x1

[0167] U y5 =U y1

[0168] U x6 =U x2

[0169] U y6 =U y2

[0170] The formulation also involves applying the force / torque balance equation:

[0171] F x1，UEL =F x1 +F x5 (101)

[0172] F y1，UEL =F y1 +F y5 (102)

[0173] F x2，UEL =F x2 +F x6 (103)

[0174] Fy2，UEL =F y2 +F y6 (104)

[0175] These formulas also include the application of seam weld / joint constraints (or “rigid inclusion” constraints) at nodes 5 and 6 at the UEL level, and also include the following equations:

[0176] UR x5 =UR x1 (105)

[0177] UR x6 =UR x2 (106)

[0178] UR y5 =UR y1 (107)

[0179] UR y6 =UR y2 (108)

[0180] U x5 =U x1 +L·UR z1 (109)

[0181] U x6 =U x2 +L·UR z2 (110)

[0182] F z1，UEL =F z1 +F z5 (111)

[0183] F z2，UEL =F z2 +F z6 (112)

[0184] M y1,UEL =M y1 +M y5 (113)

[0185] M y2,UEL =M y2 +M y6 (114)

[0186] M x1，UEL =M x1 +M x5 (115)

[0187] M x2,UEL =M x2 +M x6 (116)

[0188] Fig.15A FIG15B is a diagram of a lap fillet weld joint according to the UEL method. FIG15B is a diagram of a lap fillet weld joint according to the conventional method. The stress calculation verified by the UEL method provides a stress calculation value of 1.29 at the weld toe, and the stress calculation value of 1.29 at the weld toe is obtained by using VERITY TM The stress value for explicit seam joint modeling is calculated to be 1.27.

[0189] Fig.16A 16B is a two-element representation of a T-shaped fillet weld joint according to the UEL method with applied seam weld / joint constraints including equivalent rotation constraints in a two-dimensional cross section, and FIG. 16B is a three-element representation of a T-shaped fillet weld joint according to a conventional method. Fig.16A and FIG. 16B is used as a side view to highlight Fig.13 A and Fig.13 The local fillet weld area of ​​B. The UEL model used is a closed form analytical formula for achieving the same rotational stiffness between nodes 1, 2, and 3. The three-element model has the stiffness matrix associated with nodes 1, 2, and 3 as follows:

[0190]

[0191] Where E is the Young's modulus of the material, A ij is the cross-sectional area of ​​beam ij, I ij is the second moment of inertia of beam ij and L ij is the beam element size of beam ij.

[0192] The two-element UEL model with the stiffness matrix associated with nodes 1, 2, and 3 is as follows:

[0193]

[0194] The k1 and k2 are solved analytically by applying the following equivalent stiffness constraints:

[0195]

[0196] Equation (119) at node 1 is equivalent to the thickness t of element 2. e Solve analytically. For simplicity, t e = t, so that I 12 ′=I 12 , I 13 ′=I 13 , and the equation for node 1 is automatically satisfied. Solve the equations for nodes 2 and 3 (120 and 121) to obtain k1 and k2, such as

[0197]

[0198] where b and L represent the element dimensions along and perpendicular to the weld line, respectively, and t is the thickness of the shell element represented by UEL.

[0199] In commercial software, the unit cell shape of the UEL method can be arbitrary. For example, Fig.17 This is a graphic representation of an arbitrarily shaped node element according to the UEL method. The finite element model shape function is used, using the spatial coordinates of the weld and its surrounding nodes.

[0200] The spatial coordinates of the weld, the material properties of the plate thickness and the weld type can be input together with the UEL model into commercial modeling software such as Figure 6 The finite element analysis software outputs the stresses around the weld for use in fatigue life calculations.

[0201] Fig.18 is a bar graph comparing the stress concentration factors (SCF) of T-shaped fillet welds according to the conventional method and according to the UEL method according to the principles of the present disclosure. The reference model provides a stress concentration factor of 1.147, while the UEL model provides a stress concentration factor of 1.143 very accurately.

[0202] Fig.19 : is a validation bar graph of the maximum stress of a T-shaped fillet weld according to the conventional method, according to the coarse model using the UEL method according to the principles of the present disclosure, and the coarse model without the UEL method. The reference model provides a maximum stress of 8.58, the UEL model provides a maximum stress of 8.54 very accurately, and the coarse model without the UEL provides a maximum stress of 5.96.

[0203] Fig. 20 is a graph showing the predictability of fatigue life by combining different specimen types into narrow ranges for structures modeled with UEL coarse mesh finite elements over stress range (MPa) versus life (cycles), and Fig.21 is a graph showing that fatigue life cannot be predicted using conventional methods (e.g., nominal stress range (Mpa) versus life (cycles)). Fig. 20 The same test data shown in scatters significantly. The UEL method provides a uniform representation of fatigue test data regardless of the specimen type, number of welds present and loading pattern, etc., and therefore provides fatigue life predictions for structural durability design and assessment. The validation of the UEL technique for two fillet welded lap joints and a T-joint is summarized by comparing the calculated stress values ​​with those calculated using a mesh-insensitive structural stress method (DONG, 2010) that requires explicit fillet weld representation. The results based on UEL are in good agreement with those obtained by using a FE model with explicit seam weld representation in the FE model.

[0204] Fig. 22 is a graph of the UEL coarse mesh finite element modeling using structural stress range (Mpa) versus life (cycles) to demonstrate the predictability of fatigue life in welds of different materials (e.g., aluminum to steel), and Fig.23 It is a coordinate diagram of the conventional modeling method that uses the structural stress range (Mpa) to life (cycles) to show the predictability of fatigue life in welds of different materials (for example, aluminum to steel). Similarly, the UEL model provides a unified and consistent representation of fatigue test data of different metal joints, which cannot be achieved by existing methods.

[0205] 3. Use UEL technology to predict fatigue life

[0206] The structural stresses calculated using the developed UEL technique have been shown to integrate fatigue test data into a narrow range without the need to introduce any empirical parameters, regardless of the joint type, loading conditions and the actual number of welds involved in the component. This means that the UEL technique provides data transferability (i.e., without the need to test a large number of different joint types, specimen types, loading conditions, component geometries, etc.) and life predictability using simple joint test data to predict the fatigue life of complex structures containing many welds.

[0207] UEL techniques are used in conjunction with commercial finite element software to confirm that a structure such as a vehicle body or frame meets structural stress requirements. If it is determined that the results for a particular vehicle body design do not meet structural stress requirements, the number of locations for spot welds and / or seam welds can be modified and confirmed to meet the structural stress requirements and retested using UEL techniques. Once it is determined that the design meets the structural stress requirements, the structure can then be manufactured using the designed spot weld and / or seam weld arrangements and tested using UEL techniques.

[0208] The foregoing description of the embodiments is provided for the purpose of illustration and description. It is not intended to be exhaustive or to limit the present disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but are interchangeable where applicable and may be used in a selected embodiment even if not specifically shown or described. This may also be varied in a variety of ways. These variations should not be considered as a departure from the present disclosure, and all such modifications are intended to be included within the scope of the present disclosure.

[0209] The techniques described herein can be implemented by one or more computer programs executed by one or more processors. These computer programs include processor executable instructions stored on non-transitory tangible computer readable media. These computer programs may also include stored data. Non-limiting examples of non-transitory tangible computer readable media are non-volatile memory, magnetic storage, and optical storage.

[0210] Some portions of the above description present the techniques described herein in terms of algorithms and symbols for information operations. These algorithmic descriptions and representations are a means used by those skilled in the art of data processing to effectively convey the substance of their work to those skilled in the art. Although these operations are described functionally or logically, these operations are understood to be implemented by computer programs. In addition, without loss of generality, it sometimes proves convenient to refer to the arrangement of these operations as modules or function names.

[0211] As will be apparent from the foregoing discussion, it should be appreciated that, unless otherwise specifically noted, discussions throughout the description using terms such as "processing" or "computing" or "calculating" or "determining" or "displaying" refer to the actions and processes of a computer system or similar electronic computing device that manipulates and transforms data represented as physical (electronic) quantities in a computer system memory or registers or other such information storage, transmission or display device.

[0212] Certain aspects of the technology include process steps and instructions described herein in algorithmic form. It should be noted that the process steps and instructions described can be embodied in software, firmware or hardware, and when embodied in software, can be downloaded to be located on different platforms used by real-time network operating systems and operated from these platforms.

[0213] The present disclosure also relates to a device for performing the operations herein. The device may be specially constructed for the desired purpose, or it may include a computer selectively activated or reconfigured by a computer program stored on a computer-readable medium accessible by the computer. Such a computer program may be stored in a tangible computer-readable storage medium, such as but not limited to any type of disk, including a floppy disk, an optical disk, a compact optical disk read-only memory (CD-ROM), a magneto-optical disk, a read-only memory (ROM), a random access memory (RAM), an erasable programmable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), a magnetic card or an optical card, an application specific integrated circuit (ASIC), or any type of medium suitable for storing electronic instructions, and each is coupled to a computer system bus. In addition, the computer mentioned in the specification may include a single processor, or may be an architecture that uses a multi-processor design to increase computing power.

[0214] The algorithms and operations described herein are essentially independent of any particular computer or other device. Various systems may also be used together with programs according to the teachings herein, or it may be convenient to construct more specialized devices to perform the required method steps. For those skilled in the art, the structures required for various these systems and equivalent variations will be apparent. In addition, the present disclosure is not described with reference to any particular programming language. It should be appreciated that a variety of programming languages ​​may be used to implement the teachings of the present disclosure described herein.

Claims

1. A user unit (UEL) method for implementing a coarse grid / high fidelity computer-aided engineering (CAE) durability assessment of a point joint structure, the method comprising: providing a coarse mesh joint representation of the point joint structure; applying point joint constraints at virtual nodes represented by the coarse mesh joints; applying a membrane deformation joint constraint on the coarse mesh joint representation; The final membrane stiffness matrix expressed in closed form is applied; applying a bending deformation joint constraint on the coarse mesh joint representation; Analytically simplify the 36×36 combined stiffness matrix to a 24×24 UEL element stiffness matrix; Encoding the analytically derived stiffness matrix (24×24) in a computer programming language as a UEL subroutine for interfacing with a CAE code; and Output structural stresses around joints for durability or fatigue life prediction purposes.

2. The subscriber unit method according to claim 1, further comprising: Determining whether the point joint structure meets the required durability or fatigue life standards, and manufacturing the point joint structure.

3. The user unit method according to claim 1, wherein: The point joint constraint includes the relationship node 1: (x1, y1) = (0, a); node 2: Node 3: (x3, y3) = (b, b); Node 4: (x4, y4) = (0, b), where a = joint weld nugget radius and b = element size.

4. The user unit method according to claim 1, wherein: The membrane deformation joint constraints include rigid motion relationships.

5. The user unit method according to claim 1, wherein: The membrane deformation joint constraint includes a force balance equation.

6. The user unit method according to claim 5, wherein: The force balance equation includes F x7 =F x1 +F x2 +F x5 ; and F y7 =F y1 +F y2 +F y5 .

7. A user unit (UEL) method for implementing a coarse grid / high fidelity computer-aided engineering (CAE) durability assessment of a seam joint structure, the method comprising: providing a coarse grid joint representation of the seam joint structure; applying seam joint membrane constraints at virtual nodes represented by the coarse mesh joints; applying a seam weld joint constraint on the coarse mesh joint representation; Apply the shell element stiffness matrix expressed in closed form; Analytically simplify the 36×36 combined stiffness matrix to a 24×24 UEL element stiffness matrix; Encoding the analytically derived stiffness matrix (24×24) in a computer programming language as a UEL subroutine for interfacing with a CAE code; and Output structural stresses around seam joints for durability or fatigue life prediction purposes.

8. The subscriber unit method according to claim 7, further comprising: Determining whether the point joint structure meets the required durability or fatigue life standards, and manufacturing the point joint structure.

9. The subscriber unit method according to claim 7, wherein: The seam joint membrane constraints include rigid motion relationships.

10. The subscriber unit method according to claim 7, wherein: The seam joint membrane constraints include force / torque balance equations.

11. The subscriber unit method according to claim 7, wherein: The seam weld joint constraints include rigid inclusion constraints.

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