A coarse-model / user-element technique to enable high-fidelity computer-aided engineering durability assessment of spot-bonded structures
The UEL technique addresses the complexity and cost issues in CAE modeling of spot-coupled structures by simplifying the representation of joint stiffness, resulting in cost-effective and accurate durability assessments.
Patent Information
- Application Number
- JP2024552050
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2023-02-28
- Filing Date
- 2023-03-01
- Publication Date
- 2025-04-10
AI Technical Summary
Current CAE modeling techniques for spot-coupled structures, such as those found in vehicle bodies, are either too complex and time-consuming or too simplistic, leading to uncertainties in joint modeling and requiring excessive testing.
The use of 'User Element' (UEL) techniques to model connections, which involves strict analytical formulation to eliminate internal degrees of freedom and represent joint stiffness, allowing for simplified finite element meshes and accurate stress calculations.
UEL joint modeling significantly reduces modeling production costs by up to ten times, provides accurate stress calculations, and simplifies the modeling process, while maintaining high fidelity in durability assessments.
Smart Images
Figure 2025508951000001_ABST
Abstract
Description
[Technical field]
[0001] This application claims priority to U.S. Provisional Patent Application No. 18 / 175,756, filed February 28, 2023, and also claims the benefit of U.S. Provisional Patent Application No. 63 / 315,189, filed March 1, 2022. The entire disclosures of the foregoing applications are incorporated herein by reference.
[0002] The present disclosure relates to spot bonded (or welded, including seam welded) structures, and more particularly to user element techniques for enabling crude model / high fidelity Computer-Aided Engineering (CAE) durability assessment of such structures. [Background technology]
[0003] This section provides background information related to the present disclosure that is not necessarily prior art. This section provides a general overview of the present disclosure and is not an exhaustive disclosure of its entire scope or all of its features.
[0004] Many vehicle structures have thousands of spot welds or other types of joints (including mechanically fastened, e.g., self-piercing riveter, laser or arc welded spot or seam joints). These joints are sites of severe stress that are prone to fatigue failure under time-varying application loads, posing a major challenge in new vehicle development. Durability testing at both the component and vehicle level is too time-consuming and costly in today's competitive environment.
[0005] To ensure structural durability in rapid prototyping, reliable joint modeling methods become essential both to determine joint locations / spacing at the design stage and to minimize the physical testing required to ensure vehicle durability, often referred to as Computer Aided Engineering (CAE) or CAE durability simulation or modeling.
[0006] Currently, existing CAE modeling techniques using commercial finite element (FE) software packages suffer from the sensitivity of stress calculations around the joints to mesh size and mesh type or require explicit representation of the joint geometry (even with the most advanced methods to date). Available joint modeling scenarios are either too complex or too time consuming to be used in complex structures (e.g., containing thousands of spot joints in a typical passenger car and about 7000 in a commercial vehicle cab structure) or are too simple to produce reliable results. As a result, the uncertainties inherent in oversimplified joint modeling approaches often result in the use of many more joints than are actually necessary, requiring both exhaustive testing at various vehicle development stages. Summary of the Invention
[0007] Thus, according to the principles of the present teachings, a method is provided for modeling connections using the "User Element" (UEL) technique. In the case of spot connection modeling, the "User Element" (UEL) modeling of the present teachings is developed through a rigorous analytical formulation by eliminating a set of internal degrees of freedom to represent the actual weld or connection stiffness in the structure. As a result, a detailed ring type of finite element can be replaced by a simple finite element mesh using just four user elements to represent the spot connection, as an example. For a typical body-in-white structure containing a large number of spot connections, the use of UEL can lead to at least a ten-fold savings in modeling generation costs. In addition to significantly simplified modeling requirements, the UEL connection modeling method provides accurate stress calculation results by comparison to methods used today using mesh-insensitive structural stress methods combined with detailed explicit connection representation of the connection.
[0008] For seam welded joint modeling, the UEL method of the present teachings can also be applied for modeling seam welded joints, e.g., MIG, laser, and friction stir welding. An explicit representation of the weld fillet geometry can be represented by simple UEL plate / shell elements.
[0009] Further areas of applicability will become apparent from the description provided herein.The description and specific examples in this summary are for purposes of illustration only and are not intended to limit the scope of the disclosure.
[0010] The drawings described herein are only for purposes of illustrating selected embodiments rather than all possible implementations and are not intended to limit the scope of the present disclosure. [Brief description of the drawings]
[0011] [Figure 1] FIG. 1 shows a schematic representation of spot bonding with four "user elements" (UELs) on each of two sheets in accordance with the principles of the present disclosure. [Figure 2A] 1 is a schematic illustration of an existing explicit spot bond modeling technique according to the VERITY™ method available in one of the commercial durability software. It should be noted that other available methods that use bond representations that are illustrated but do not have conventional elements, such as the LBF method, fail to produce reliable stress results. [Figure 2B] 1 is a schematic illustration of an existing explicit spot bond modeling technique according to the VERITY™ method available in one of the commercial durability software. It should be noted that other available methods that use bond representations that are illustrated but do not have conventional elements, such as the LBF method, fail to produce reliable stress results. [Diagram 3]FIG. 13 illustrates a comparison of a conventional 36×36K matrix of virtual nodes of an existing explicit spot-bond modeling technique using the present coarse-mesh / high-fidelity computer-aided design durability assessment against an analytically reduced 24×24K matrix of virtual nodes by imposing spot-bond constraints according to the principles of the present disclosure. [Figure 4] 1 is an illustration of virtual nodes 1, 2, and 5 of the K matrix with thin film junction constraints 7-1, 7-2, 7-5 imposed in accordance with the principles of the present disclosure. [Diagram 5] FIG. 1 is a schematic diagram of an implementation of the UEL in finite element software. [Figure 6] 1 is an illustration of an example ABAQUS™ user subroutine interface in accordance with the principles of the present disclosure. [Figure 7A] 1 is an illustration of a component containing two spot welds modeled according to an existing direct method, e.g., VERITY™. [Figure 7B] 1 is an illustration of a component containing two spot welds modeled according to the UEL method. [Figure 8] 1 is a first comparative graph of stress per unit load versus angle (in degrees) around a spot weld end by a direct stress test method, a UEL method in accordance with the principles of the present disclosure, and a traditional "LBF" method used in various commercial structural durability software packages which also allows for a simple joint representation, but lacks the necessary accuracy. [Figure 9A] 1 is an illustration of a component containing two spot bonds under lap shear loading by a direct method, e.g., VERITY™. [Figure 9B] 1 is an illustration of a component with two spot bonds in a lap shear specimen using the UEL method. [Figure 10]13 is a second comparison graph of stress concentration factor (SCF) versus angle (in degrees) for lap shear specimens using the direct stress test method, the UEL method according to the principles of the present disclosure, and the traditional "LBF" method used in a commercial structural durability software package. [Figure 11A] Figure 11A (left) is a schematic three-dimensional (3D) representation of a seam-welded component with 3D fillet welds (having a triangular cross-section) using UEL from existing explicit weld modeling techniques in today's structural durability simulation software. Figure 11A (right) is a schematic representation of the same 3D component using UEL where only plate or shell elements are needed without loss of accuracy. [Figure 11B] Figure 11B (left) is a representation of a finite element model using solid elements with an explicit fillet weld representation, and Figure 11B (right) is a representation of a finite element model using UEL, which allows for a simple representation of fillet welds with the same computational accuracy. [Figure 12] 1 is a schematic illustration of existing explicit T-joint seam weld modeling techniques for representing actual 3D plate fillet weld components in structures. [Figure 13] Figure 13 (left) is a schematic representation of a finite element model using solid elements with an explicit fillet weld representation, and Figure 13 (right) is a schematic representation of a T-joint seam weld modeling using UEL, where not only does the 3D fillet weld not need to be modeled, but simple shell or plate elements are sufficient. [Figure 14A] 1 is an illustration of the actual nodes (5 and 6) of a conventional seam welded joint modeling technique with two plate elements in existing structural durability software. [Figure 14B] FIG. 14B is an illustration of how the two real nodes of FIG. 14A are eliminated in the UEL by imposing a seam bond thin film constraint via two virtual nodes in the UEL formulation according to the principles of the present disclosure. [Figure 15A]This is an illustration of a lap fillet weld joint using the UEL method. [Figure 15B] 1 is an illustration of a lap fillet welded joint according to a conventional method. [Figure 16A] FIG. 13C is a side view of FIG. 13B; [Figure 16B] FIG. 13B is a side view of a three element representation of a T-fillet welded joint according to the prior art; [Figure 17] 13 is an illustration of an arbitrary shaped four-node element using the UEL method to represent spots within a complex structure. [Figure 18] 1 is a comparative bar graph of stress concentration factors (SCF) of T-fillet welded components by conventional methods and by UEL methods in accordance with the principles of the present disclosure; [Figure 19] 13 is a validation bar graph of highest stress calculated for a T-fillet welded component according to a conventional method, according to a crude model with the UEL method according to the principles of the present disclosure, and using a crude model without the UEL method; [Figure 20] 1 is a graph showing fatigue life predictability with structural stress range (MPa) versus life (cycles) using UEL-based coarse-mesh finite element modeling. [Figure 21] 1 is a graph showing fatigue life predictability with nominal stress range (MPa) versus life (cycles) for conventional modeling methods. [Figure 22] 1 is a graph showing fatigue life predictability in dissimilar material welds such as aluminum to steel using structural stress range (MPa) versus life (cycles) for UEL coarse mesh finite element modeling. [Figure 23] 1 is a graph showing fatigue life predictability in dissimilar material welds such as aluminum to steel using structural stress range (MPa) versus life (cycles) for conventional modeling methods. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0012] Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.
[0013] Example embodiments will now be described more fully with reference to the accompanying drawings.
[0014] The illustrative examples are provided so that the present disclosure will be complete and will fully convey the scope of the present disclosure to those skilled in the art. Many specific details, such as examples of specific components, devices, and methods, are set forth in order 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, that the illustrative embodiments can be implemented in many different forms, and that none of these should be construed as limiting the scope of the present disclosure. In some illustrative examples, well-known processes, well-known device structures, and well-known techniques are not described in detail.
[0015] The terminology used herein is merely for the purpose of describing particular illustrative embodiments and is not intended to be limiting. As used herein, the singular forms "a," "an," and "the" may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises," "comprising," "including," and "having" are inclusive and thus specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. The steps, processes, and operations of the methodologies described herein should not necessarily be construed as requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also understood that additional or alternative steps may be employed.
[0016] Terms such as first, second, third, etc. may be used herein to describe various elements, components, regions, layers, and / or sections, but these elements, components, regions, layers, and / or sections should not be limited by these terms. These terms may be used merely to distinguish one element, component, region, layer, or section from another region, layer, or section. As used herein, terms such as "first", "second", and other numerical terms do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer, or section described below may be referred to as a second element, component, region, layer, or section without departing from the teachings of the illustrative embodiments.
[0017] 1. Spot bond modeling "User Elements" (UELs) were developed through a rigorous formulation by eliminating a set of internal degrees of freedom at virtual nodes that represent the actual weld or joint stiffness in the vehicle body structure. The welds modeled can be welds connecting components such as, but not limited to, front rails, side rails, rear rails, floor components, firewall components, floor cross members, roof cross members, A-pillars, B-pillars, and other body components. The resulting UEL joint representation in a complex structure can be as simple as Figure 1 or Figure 11A (right) or Figure 13B with a simplified UEL joint connecting between two plates.
[0018] 2A and 2B are two illustrations of spot bond representations using existing explicit spot bond modeling techniques in today's commercially available structural durability software, e.g., VERITY™, for a spot bond between two plates (FIG. 2A shows a view of the top plate, and FIG. 2B is a cross-sectional cutaway view of cross section AA as shown in FIG. 2A).
[0019] 3 is a schematic illustration for developing a UEL for modeling a quarter of a spot weld. Actual nodes 1, 2, and 5 in the conventional 36×36K matrix of the existing explicit spot joint modeling technique using the present coarse mesh / high fidelity computer-aided design durability assessment are replaced as virtual nodes (left) so that the internal degrees of freedom at the virtual nodes can be eliminated by imposing the dashed spot joint constraints according to the principles of the present disclosure (right), leading to an analytically reduced 24×24K matrix.
[0020] The process of analysis to produce the UEL formulation is now described with reference to Figures 3 and 4. The UEL formulation involves imposing spot joint constraints at virtual nodes (1, 2 and 5). Shell / plate elements in commercial finite element codes such as ABAQUS are thin-film K m and Plate K b The plate membrane element has two degrees of freedom at each node, i.e., u, v, where u, v, and w represent the displacements along the X, Y, and Z directions. The plate bending element has two degrees of freedom at each node, i.e., w, θ x , θ y , where θ x , θ y represents a rotation along the X and Y directions. The coordinates of nodes 1, 2, 3, and 4 in this example are:
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[0021] The UEL formulation further includes imposing a membrane junction constraint in the equation:
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[0022] The membrane connection constraints applied include rigid body kinematic relations:
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[0023] The UEL formulation is m results in a 12 × 12 matrix. The additional excavation degrees of freedom θ z is added for numerical stability.
[0024] The UEL formulation provides two shell elements (eg, "S4" in ABAQUS), part 1, imposing thin-film joint constraints. The displacement vector can be expressed as:
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[0025] The final membrane stiffness matrix K without drilling degrees of freedom expressed in closed form m The UEL formulation for (8×8) is:
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[0026] The complete expression of this equation is shown below:
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[0027] The UEL formulation involves imposing joint bending constraints in the following equations:
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[0028] The rigid body kinematic equations / constraints include:
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[0029] The force / moment equilibrium equations / constraints include:
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[0030] The joint bending constraint equation is expressed as:
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[0031] The end result of the UEL method can be used directly through user interfaces available in major commercial finite element software vendors (e.g., ABAQUS™). As an example for demonstration purposes, the implementation of the UEL technique in ABAQUS™ as a User Element Subroutine (UEL) in Figures 5 and 6, where: U = displacement, AMATRX = UEL stiffness matrix, and RHS=force / moment vector.
[0032] As such, after gaining access to the UEL subroutine, any user of a commercial FE software package can treat the UEL just like a regular element in their element library to perform their own Computer Aided Engineering (CAE) structural analysis. The UEL models the calculation and use of UEL data in a commercial finite element software package. Specifically, it writes all 24x24 entries of the UEL stiffness matrix K into an array "AMTRX" on the left, for example k(1,1) above. A valid UEL Fortran code is fitted with ABAQUS™ for a large number of spot welded components.
[0033] The stresses around the joints, essential for structural durability or fatigue assessment, can then be calculated by using the nodal forces and nodal moments available at the internal virtual nodes of the UEL elements, by invoking two well-documented methods. The two methods for calculating structural stresses in joints with demonstrated mesh size insensitivity include:
[0034] Method 1: Decompose the nodal forces / moments into a set of simple loading modes for which analytical solutions are available, and then superimpose them into a comprehensive 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):107-109).
[0035] Method 2: Apply the simultaneous equations method (see Zhang et al. 2022) by transforming the nodal forces / moments about virtual nodes into line forces / moments. The structural stresses around the joint can be calculated using the line forces divided by the plate thicknesses and line moments by the plate section moduli.
[0036] The effectiveness and simplicity of the UEL modeling method was demonstrated on a number of spot welded components under various loading conditions as shown in Figures 7A and 7B. Figure 7A is an illustration of a two spot joint by the direct method. Figure 7B is an illustration of a two spot joint modeled according to the UEL method. Figure 8 is a first comparative graph of stress per unit load versus angle (degrees) by the direct stress testing method, the UEL method according to the principles of the present disclosure, and the traditional "LBF" method used in commercial computer-aided engineering software. The correct solution (labeled as the "direct method" using a fairly complex joint representation) is obtained by the most advanced, mesh-insensitive method (Dong, P., JK Hong, DAO Sage, DJ Dewees, and M. Prager. "The master SN curve method an implementation for fatigue evaluation of welded components in the ASME B&PV Code, Section VIII, Division 2 and API 579-1 / ASME FFS-1". Welding Research Council Bulletin 523 (2010)), which is not suitable for modeling a large number of spot connections in complex structures. In all cases the solutions using the UEL technique do not show significant deviations from the reference solution. All other solutions available in the literature and in commercial finite element codes fail to provide a reasonable solution.
[0037] As a further validation technique, FIG. 9A is an illustration of a two-spot bond in a lap shear specimen using the direct method. FIG. 9B is an illustration of a two-spot bond in a lap shear specimen using the UEL method. FIG. 10 is a second comparison graph of Stress Concentration Factor (SCF) vs. Angle (degrees) for lap shear specimens using the direct stress testing method, the UEL method according to the principles of the present disclosure, and the traditional "LBF" method used in commercial computer-aided engineering software. Furthermore, in all cases the solutions using the UEL technique do not show significant deviations from the reference "direct method" solutions.
[0038] 2. Seam welded joint modeling The aforementioned UEL technique may be suitable for modeling seam joints, for example, by friction-based welding or joining, including fusion welding processes, for example, laser beam welding (LBW), metal inert gas (MIG) or other solid-state welding processes, for example, friction stir welding (FSW), etc. FIGS. 11A and 11B are schematic representations of the development of a seam weld model using UEL from an existing explicit parallel seam weld joint modeling technique using coarse mesh / high fidelity computer-aided design durability evaluation of automotive structures. Similarly, FIG. 12 is a schematic illustration of an existing explicit T-joint seam weld modeling technique using coarse mesh / high fidelity computer-aided design durability evaluation of automotive structures, and FIGS. 13A and 13B are schematic representations of T-joint seam weld modeling using explicit fillet weld representation and using UEL, respectively. FIG. 14 is an illustration of a virtual node of a conventional seam weld joint modeling technique with imposed seam joint thin film constraints to provide a virtual node of a UEL node in accordance with the principles of the present disclosure.
[0039] The decomposition of the shell element stiffness matrix is:
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[0040] Imposing a seam joint membrane constraint requires the collection of two membrane element stiffness matrices and the application of a constraint involving the following rigid body kinematic relations:
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[0041] The formulation also includes imposing seam weld / joint constraints (or "rigid inclusion" constraints) at nodes 5 and 6, and the UEL level further includes the following equations:
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[0042] Figure 15A is an illustration of a lap and fillet welded joint using the UEL method. Figure 15B is an illustration of a lap and fillet welded joint using the conventional method. Stresses calculated as validation of the UEL method provided stress calculations at the weld toe in 1.29 and stress calculations using explicit seam joint modeling using Verity™ in 1.27.
[0043] FIG. 16A is a two-element representation of a T-fillet welded joint with the UEL method imposing 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-fillet welded joint with the conventional method. FIGS. 16A and 16B serve as side views to highlight the local fillet welded regions of FIGS. 13A and 13B. The UEL model used is a closed-form analytical formulation to achieve the same rotational stiffness between nodes 1, 2 and 3. The three-element model has stiffness matrices associated with nodes 1, 2 and 3 as follows:
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[0044] The two-element UEL model for the stiffness matrix associated with nodes 1, 2 and 3 is:
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[0045] In commercial software, the shape of elements in the UEL method can be arbitrary. For example, FIG. 17 is an illustration of an arbitrary shape node element in the UEL method. Using the finite element model shape functions, the spatial coordinates of the weld and surrounding nodes are adopted.
[0046] The spatial coordinates of the weld, material properties of the plate thickness and type weld can be input into commercial modeling software along with the UEL model as shown in Figure 6. The finite element analysis software outputs the stresses around the weld for fatigue life calculations.
[0047] 18 is a comparative bar graph of stress concentration factors (SCF) of a T-fillet welded component according to the conventional method and the UEL method according to the principles of the present disclosure. The reference model provided a stress concentration factor of 1.147, while the UEL model provided a very accurate stress concentration factor of 1.143.
[0048] 19 is a validation bar graph of the highest stress of a T-fillet welded component with the conventional method, with the crude model with the UEL method according to the principles of the present disclosure, and using the crude model without the UEL method. The reference model provided a highest stress of 8.58, the UEL model very accurately provided a highest stress of 8.54, and the crude model without the UEL provided a highest stress of 5.96.
[0049] FIG. 20 is a graph showing fatigue life predictability of structural stress range (MPa) versus life (cycles) for UEL coarse mesh finite element modeling by integrating different specimen types into narrow bands, and FIG. 21 is a graph showing the inability of fatigue life prediction using conventional methods, e.g., nominal stress range (MPa) versus life (cycles), where the same test data shown in FIG. 20 is significantly scattered. The UEL method provides a unified presentation of fatigue test data regardless of specimen type, number of welds present, and loading mode, etc., and therefore provides fatigue life predictability for structural durability design and assessment. Validation of the UEL technique for two fillet welded lap joints and a T-joint is summarized by comparing the stress values calculated with those using a mesh-insensitive structural stress method (Dong, 2010), which requires explicit fillet weld representation. The UEL-based results are in good agreement with the results obtained by using a FE model with explicit seam weld representation in the FE model.
[0050] Figure 22 is a graph showing fatigue life predictability in dissimilar material welds, such as aluminum to steel, with structural stress range (MPa) versus life (cycles) for UEL coarse mesh finite element modeling, and Figure 23 is a graph showing fatigue life predictability in dissimilar material welds, such as aluminum to steel, with structural stress range (MPa) versus life (cycles) for traditional modeling methods. Again, the UEL model provided a unified and consistent representation of fatigue test data for dissimilar metal joints, which none of the existing methods can do.
[0051] 3. Fatigue life predictability using UEL techniques The structural stresses so calculated using the developed UEL technique have been proven to integrate fatigue test data in a narrow band without introducing empirical parameters, regardless of the joint type, loading conditions, and the actual number of welds involved in the components. This implies that the UEL technique provides both data portability (i.e., no need to test large variations in joint types, specimen types, loading conditions, component geometries, etc.) and life predictability to predict fatigue lives of complex structures containing multiple welds using simple joint test data.
[0052] The UEL technique is used with commercial finite element software to verify that a structure, such as a vehicle body or frame, meets the structural stress requirements. If the results of a particular body design are determined to not meet the structural stress requirements, the number of spot and / or seam weld locations may be modified and verified to meet the structural stress requirements and retested using the UEL technique. After the design is determined to meet the structural stress requirements, the structure may then be manufactured with the spot and / or seam weld configuration as designed and tested using the UEL technique.
[0053] The foregoing description of the embodiments has been provided for purposes 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 a particular embodiment, but may be interchangeable, where applicable, and may be used in selected embodiments even if not specifically shown or described. Individual elements or features of the same particular embodiment may also be modified in numerous ways. Such variations should not be considered as departures from the present disclosure, and all such modifications are intended to be included within the scope of the present disclosure.
[0054] The techniques described herein may be implemented by one or more computer programs executed by one or more processors. The computer programs include processor-executable instructions stored on a non-transitory tangible computer-readable medium. The computer programs may also include stored data. Non-limiting examples of non-transitory tangible computer-readable media are non-volatile memory, magnetic storage devices, and optical storage devices.
[0055] Some portions of the preceding description present the techniques described herein in terms of algorithms and symbolic representations of operations related to information. These algorithmic descriptions and representations are the means used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. While described functionally or logically, these operations will be understood to be implemented by computer programs. In addition, it has also proven convenient at times to refer to these arrangements of operations as modules or by functional names, without loss of generality.
[0056] Unless specifically indicated otherwise as is clear from the preceding discussion, discussion throughout this specification using terms such as "processing" or "calculating" or "calculating" or "determining" or "displaying" will be understood to 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 the computer system memory or registers or other such information storage, transmission or display devices.
[0057] Certain aspects of the described techniques include process steps and instructions described herein in the form of an algorithm. It should be noted that the described process steps and instructions may be implemented in software, firmware, or hardware, and when implemented in software, may be downloaded to reside on and operated from different platforms used by the real-time network operating system.
[0058] The present disclosure also relates to an apparatus for performing the operations herein. The apparatus may be specifically constructed for the required purposes, or the apparatus may include a computer selectively activated or reconfigured by a computer program stored in 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, a floppy disk, an optical disk, a CD-ROM, any type of disk including a magneto-optical disk, a read-only memory (ROM), a random access memory (RAM), an EPROM, an EEPROM, a magnetic or optical card, an application specific integrated circuit (ASIC), or any type of medium suitable for storing electronic instructions and each coupled to a computer system bus. Additionally, the computers referred to herein may include a single processor or may be architectures employing multiple processor designs for increased computing power.
[0059] The algorithms and operations presented herein are not inherently related to any particular computer or other apparatus. A variety of systems may also be used with programs in accordance with the teachings herein, or it may prove convenient to construct more specialized apparatus to perform the required method steps. The required structure for a variety of these systems, along with equivalent variations, will be apparent to those skilled in the art. Further, the present disclosure is not described with reference to any particular programming language. It will be understood that a variety of programming languages may be used to implement the teachings of the present disclosure as described herein.
Claims
1. 1. A User Element (UEL) methodology for enabling coarse mesh / high fidelity Computer Aided Engineering (CAE) durability assessment of spot bonded structures, comprising: providing a coarse-mesh connectivity representation of the spot-connected structure; imposing spot connection constraints at virtual nodes of the coarse-mesh connection representation; imposing thin film deformation connection constraints on the coarse mesh connection representation; imposing a final membrane stiffness matrix expressed in closed form; imposing a bending deformation bond constraint on the coarse mesh bond representation; Analytical reduction of the 36×36 combined stiffness matrix to a 24×24 UEL element stiffness matrix; coding, in a computer programming language, the analytically derived stiffness matrix (24×24) into a UEL subroutine for interfacing with a CAE code; Outputting structural stresses around the joint for durability or fatigue life prediction purposes; A user element method comprising:
2. The user element method of claim 1 , further comprising: determining whether the spot bonded structure meets required durability or fatigue life criteria; and manufacturing the spot bonded structure.
3. The spot join constraint is that the relation node 1:(x １ , y １ ) = (0, a), node 2: [0010] , Node 3: (x ３ , y ３ )=(b,b), Node 4: (x ４ , y ４ 2. The user element method of claim 1, wherein a=joint weld nugget radius and b=element size.
4. The user element method of claim 1 , wherein the thin film deformation joint constraint comprises a rigid body kinematic relationship.
5. The user element method of claim 1 , wherein the membrane deformation bond constraints include force balance equations.
6. The force balance equation is: F ｘ７ = F ｘ１ +F ｘ２ +F ｘ５ and F ｙ７ = F ｙ１ +F ｙ２ +F ｙ５ The user element method of claim 5 , comprising:
7. 1. A User Element (UEL) methodology for enabling coarse mesh / high fidelity computer-aided engineering (CAE) durability assessment of seam-bonded structures, comprising: providing a coarse mesh joint representation of the seam-jointed structure; imposing seam bond thin film constraints at virtual nodes of the coarse mesh bond representation; imposing a seam weld joint constraint on the coarse mesh joint representation; imposing a shell element stiffness matrix expressed in closed form; Analytical reduction of the 36×36 combined stiffness matrix to a 24×24 UEL element stiffness matrix; coding, in a computer programming language, the analytically derived stiffness matrix (24×24) into a UEL subroutine for interfacing with a CAE code; Outputting structural stresses around seam connections for durability or fatigue life prediction purposes; A user element method comprising:
8. The user element method of claim 7 , further comprising: determining whether the spot bonded structure meets required durability or fatigue life criteria; and manufacturing the spot bonded structure.
9. The user element method of claim 7 , wherein the seam bond membrane constraint comprises a rigid body kinematic relationship.
10. The user element method of claim 7 , wherein the seam bond membrane constraints include force / moment balance equations.
11. The user element method of claim 7 , wherein the seam weld joint constraint comprises a rigid inclusion constraint.