A dimension expansion-based nonlinear unit construction method
By expanding new nodes to form three-dimensional solid elements for shell elements, the problems of low accuracy and high computational burden of shell elements in the existing technology are solved, realizing an efficient three-dimensional analysis system and improving the accuracy and efficiency of aerospace structural design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA AIRPLANT STRENGTH RES INST
- Filing Date
- 2026-04-23
- Publication Date
- 2026-06-23
AI Technical Summary
In aerospace structural design, existing technologies based on classical beam and plate/shell theories have low accuracy in element models, making it difficult to accurately describe the actual displacement field. Furthermore, they are prone to shear locking problems when simulating bending deformation, especially in thin-walled structures where the computational burden is too heavy.
By assigning a number to each shell element, new nodes are expanded to form three-dimensional solid elements, establishing a unified three-dimensional isoparametric element framework, mapping the mechanical behavior of shell elements to three-dimensional space, realizing direct coupling of different shell elements, and forming a complete three-dimensional analysis system.
It significantly improves the accuracy and boundary adaptability of shell elements, reduces the difficulty of developing nonlinear elements, and improves simulation efficiency.
Smart Images
Figure CN122072776B_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of electrical data processing technology, and specifically relates to a method for constructing nonlinear units based on dimensional expansion. Background Technology
[0002] Structural nonlinear analysis is a key method for investigating the ultimate bearing capacity of complex structures under extreme loads, especially in thin-walled structures widely used in the aerospace field, where post-buckling behavior and failure mechanisms heavily rely on accurate nonlinear analysis. Therefore, developing efficient, stable, and accurate nonlinear analysis theories and tools has become a core research direction in the field of aerospace structural design and performance evaluation.
[0003] Typical aerospace structures such as aircraft wings and fuselages are mainly composed of thin-walled and slender components. Directly modeling these structures using 3D solid elements requires extremely dense meshing to capture their geometric features, resulting in high computational costs. Furthermore, low-order solid elements are prone to shear locking issues when simulating bending deformation, while using high-order or non-conforming elements further exacerbates the computational burden. In contrast, modeling based on beam and shell elements can significantly reduce the computational scale and improve simulation efficiency.
[0004] The construction of classical beam and plate shell theoretical elements (based on displacement compatibility mode) usually follows these steps: ① Define the element configuration based on deformation assumptions; ② Substitute it into the three-dimensional finite deformation theory to obtain the equilibrium equations; ③ Derive the strain measure conjugate with stress work through variational principle and virtual work principle; ④ Establish constitutive relations; ⑤ Discretize and linearize the virtual work equations to obtain the element tangent stiffness matrix and internal force vector; ⑥ Update the element configuration according to incremental displacement.
[0005] However, elements constructed based on the aforementioned theoretical framework have significant limitations. These elements typically rely on displacement interpolation and strict displacement compatibility conditions, but because the assumed shape functions often fail to accurately describe the actual displacement field, the element accuracy is low, often requiring dense meshes to meet computational requirements. For example, when using four-node quadrilateral elements to simulate bending problems, shear locking easily occurs when the mesh is sparse. Furthermore, traditional methods are primarily designed for continuums and have poor adaptability to discontinuous problems. Summary of the Invention
[0006] To address the aforementioned problems, this application provides a method for constructing nonlinear units based on dimension expansion, comprising:
[0007] Step S1: Assign a number to each shell element in the finite element model and assign an index number to each node that makes up each shell element; store all nodes of all shell elements in a global node array in sequence; divide the node sequence into node subarrays that correspond one-to-one with each shell element according to the starting position of each shell element's node in the global node array.
[0008] Step S2: Calculate the normal vector of each shell element and obtain the thickness and offset parameters of each shell element; take the normal of one shell element as the reference normal, and group the shell elements whose normal and the reference normal are less than a preset angle and whose thickness and offset are the same into a subset, which are considered to have a consistent normal.
[0009] Step S3: For each subset with a consistent normal obtained in step S2, take each node in the subset as the starting point, and extend a new node in both the positive and negative directions along the normal of the subset shell unit. The distance between each new node and the starting point is half the thickness of the subset shell unit.
[0010] Step S4: Identify nodes belonging to at least two different shell elements and define them as common nodes; take each common node as a starting point and extend a new node in both the positive and negative directions along the normal of each shell element to which it belongs. The distance between each new node and the starting point is half the thickness of the corresponding shell element; define all new nodes extended from the same common node as a knot.
[0011] Step S5: Taking the nodes not covered by steps S3 and S4 as the starting point, extend a new node in both the positive and negative directions along the normal of the shell element to which it belongs. The distance between each new node and the starting point is half the thickness of the corresponding shell element.
[0012] Step S6: For each shell element, based on all its related new nodes, form the corresponding three-dimensional solid element according to the node topology rules of the three-dimensional solid element.
[0013] Step S7: Apply the pre-defined constraints applied to the common nodes to the nodes corresponding to the common nodes; apply the pre-defined constraints applied to the non-common nodes to the new nodes extended from the nodes.
[0014] Preferably, in step S1, the global node array is denoted as the elmnodes array, and the starting position of each shell unit within it is recorded using the expnodesIP array; the node subarray elmnodes(i) of the i-th shell unit is determined from the elmnodes array according to the starting position expnodesIP(i) of the i-th shell unit.
[0015] Preferably, all new nodes are added to the node subarray of their corresponding shell unit.
[0016] Preferably, when the constraint applied to the common node includes a rotational degree of freedom constraint, the rotational degree of freedom constraint is applied to the rotational node of the corresponding node.
[0017] Preferably, the method further includes step S8: when there is a knot at the connection position of the finite element model, the connection is guaranteed by the knot; when there is no knot at the connection position, multi-point constraint equations are created to restore the user-defined original connection relationship.
[0018] Preferably, the preset angle is 0.5°.
[0019] Preferably, in S6, the three-dimensional solid unit is a three-dimensional isoparametric solid unit.
[0020] This application establishes a unified three-dimensional isoparametric element framework, mapping the mechanical behavior of two-dimensional shell elements to three-dimensional space, realizing direct coupling of different shell elements, forming a complete three-dimensional analysis system, significantly improving the accuracy and boundary adaptability of shell elements, and greatly reducing the difficulty of developing nonlinear elements. Attached Figure Description
[0021] Figure 1 This is a schematic diagram of the finite element model of the wing beam structure.
[0022] Figure 2 This is a schematic diagram of a shell element and its normal.
[0023] Figure 3 This is a schematic diagram of a three-dimensional solid unit.
[0024] Figure 4 This is a schematic diagram of expanding a new node from a node in a shell element. Detailed Implementation
[0025] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.
[0026] This application provides a method for constructing nonlinear units based on dimension expansion, such as... Figures 1-4 As shown, it includes:
[0027] Step S1: Assign a number to each shell element in the finite element model and assign an index number to each node that makes up each shell element; store all nodes of all shell elements in a global node array in sequence; divide the node sequence into node subarrays that correspond one-to-one with each shell element according to the starting position of each shell element's node in the global node array.
[0028] Step S2: Calculate the normal vector of each shell element and obtain the thickness and offset parameters of each shell element; take the normal of one shell element as the reference normal, and group the shell elements whose normal and the reference normal are less than a preset angle and whose thickness and offset are the same into a subset, which are considered to have a consistent normal.
[0029] Step S3: For each subset with a consistent normal obtained in step S2, take each node in the subset as the starting point, and extend a new node in both the positive and negative directions along the normal of the subset shell unit. The distance between each new node and the starting point is half the thickness of the subset shell unit.
[0030] Step S4: Identify nodes belonging to at least two different shell elements and define them as common nodes; take each common node as a starting point and extend a new node in both the positive and negative directions along the normal of each shell element to which it belongs. The distance between each new node and the starting point is half the thickness of the corresponding shell element; define all new nodes extended from the same common node as a knot.
[0031] Step S5: Taking the nodes not covered by steps S3 and S4 as the starting point, extend a new node in both the positive and negative directions along the normal of the shell element to which it belongs. The distance between each new node and the starting point is half the thickness of the corresponding shell element.
[0032] Step S6: For each shell element, based on all its related new nodes, form the corresponding three-dimensional solid element according to the node topology rules of the three-dimensional solid element.
[0033] Step S7: Apply the pre-defined constraints applied to the common nodes to the nodes corresponding to the common nodes; apply the pre-defined constraints applied to the non-common nodes to the new nodes extended from the nodes.
[0034] In some optional implementations, in step S1, the global node array is denoted as the elmnodes array, and the starting position of each shell unit within it is recorded using the array expnodesIP; the node subarray elmnodes(i) of the i-th shell unit is determined from the elmnodes array according to the starting position expnodesIP(i) of the i-th shell unit.
[0035] In some alternative implementations, all new nodes are added to the node subarray of their corresponding shell unit.
[0036] In some alternative implementations, when the constraint applied to the common node includes a rotational degree of freedom constraint, the rotational degree of freedom constraint is applied to the rotational node of the corresponding node.
[0037] In some optional implementations, the method further includes step S8: when a knot exists at the connection location of the finite element model, the connection is guaranteed by the knot; when no knot exists at the connection location, multi-point constraint equations are created to restore the user-defined original connection relationship.
[0038] In some alternative implementations, the preset angle is 0.5°.
[0039] In some alternative implementations, in S6, the three-dimensional solid element is a three-dimensional isoparametric solid element.
[0040] This application establishes a unified three-dimensional isoparametric element framework, mapping the mechanical behavior of two-dimensional shell elements to three-dimensional space, realizing direct coupling of different shell elements, forming a complete three-dimensional analysis system, significantly improving the accuracy and boundary adaptability of shell elements, and greatly reducing the difficulty of developing nonlinear elements.
[0041] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for constructing nonlinear units based on dimensional expansion, characterized in that, include: Step S1: Assign a number to each shell element in the finite element model and assign an index number to each node that makes up each shell element; store all nodes of all shell elements in a global node array in sequence; divide the node sequence into node subarrays that correspond one-to-one with each shell element according to the starting position of each shell element's node in the global node array. Step S2: Calculate the normal vector of each shell element and obtain the thickness and offset parameters of each shell element; take the normal of one shell element as the reference normal, and group the shell elements whose normal and the reference normal are less than a preset angle and whose thickness and offset are the same into a subset, which are considered to have a consistent normal. Step S3: For each subset with a consistent normal obtained in step S2, take each node in the subset as the starting point, and extend a new node in both the positive and negative directions along the normal of the subset shell unit. The distance between each new node and the starting point is half the thickness of the subset shell unit. Step S4: Identify nodes belonging to at least two different shell elements and define them as common nodes; take each common node as a starting point and extend a new node in both the positive and negative directions along the normal of each shell element to which it belongs. The distance between each new node and the starting point is half the thickness of the corresponding shell element; define all new nodes extended from the same common node as a knot. Step S5: Taking the nodes not covered by steps S3 and S4 as the starting point, extend a new node in both the positive and negative directions along the normal of the shell element to which it belongs. The distance between each new node and the starting point is half the thickness of the corresponding shell element. Step S6: For each shell element, based on all its related new nodes, form the corresponding three-dimensional solid element according to the node topology rules of the three-dimensional solid element. Step S7: Apply the pre-defined constraints applied to the common nodes to the nodes corresponding to the common nodes; apply the pre-defined constraints applied to the non-common nodes to the new nodes extended from the nodes.
2. The method for constructing nonlinear units based on dimension expansion according to claim 1, characterized in that, In step S1, the global node array is denoted as the elmnodes array, and the starting position of each shell unit within it is recorded using the expnodesIP array; the node subarray elmnodes(i) of the i-th shell unit is determined from the elmnodes array based on the starting position expnodesIP(i) of the i-th shell unit.
3. The method for constructing nonlinear units based on dimension expansion according to claim 2, characterized in that, Add all new nodes to the node subarray of their corresponding shell unit.
4. The method for constructing nonlinear units based on dimension expansion according to claim 1, characterized in that, When the constraint applied to a common node includes a rotational degree of freedom constraint, that rotational degree of freedom constraint is applied to the rotational node of the corresponding node.
5. The method for constructing nonlinear units based on dimension expansion according to claim 1, characterized in that, The method further includes step S8: when there is a knot at the connection position of the finite element model, the connection is guaranteed by the knot; when there is no knot at the connection position, multi-point constraint equations are created to restore the user-defined original connection relationship.
6. The method for constructing nonlinear units based on dimension expansion according to claim 1, characterized in that, The preset angle is 0.5°.
7. The method for constructing nonlinear units based on dimension expansion according to claim 1, characterized in that, In S6, the three-dimensional solid unit is a three-dimensional isoparametric solid unit.