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Meshless solid mechanical simulation method, electronic equipment and storage medium
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A technology of solid mechanics and simulation method, which is applied in the field of mechanical simulation system, can solve problems such as difficult fracture and crushing, and achieve the effect of improving calculation efficiency and simulation accuracy
Active Publication Date: 2019-12-10
BEIHANG UNIV
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[0006] In order to overcome the deficiencies of the prior art, one of the purposes of the present invention is to provide a meshless solidmechanics simulation method, which can improve the calculation efficiency and simulation accuracy, It is also beneficial to solve the problem that traditional simulation methods are difficult to simulate extreme problems such as fracture and broken
[0007]The second purpose of the present invention is to provide an electronic device, which can improve the calculation efficiency and simulation accuracy, and is beneficial to solve the problem that traditional simulation methods are difficult to break, break, etc. The Difficulty of Extreme Problem Simulation
[0008]The third purpose of the present invention is to provide a computer-readable storage medium, which can improve the calculation efficiency and simulation accuracy, and is beneficial to solve the problem that the traditional simulation method is difficult to break , broken and other extreme problem simulation problems
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Embodiment approach 1
[0116] For such as Figure 7 The structure shown:
[0117] Step C11: First, divide the structure into several sub-domains by using randomly distributed nodes in the structure.
[0118] Step C12: Determine the support domain of each node, and use the weighted least square method to calculate the expressions of the test function and inspection function in each sub-domain in the structure.
[0119] Among them, the test function: u h = Nu E , N is the shape function, u E is the node displacement.
[0120] Test function: v=Nv E , has the same shape function N as the test function.
[0121] Step C13: Introduce numerical flux correction to obtain the Galerkin weak form with numerical flux correction.
[0122] Step C14: Substitute the test function and test function of each subdomain into the Galerkin weak form with numerical flux correction. That is to formula (7), and then use the Gaussianintegral method to perform numerical integration to obtain the node stiffness matrix K...
Embodiment approach 2
[0128] For such as Figure 10 The shown planar structure with cracks:
[0129] Step C21: Divide the structure into several subdomains according to the same subdomain division method.
[0130] Step C22: Determine the support domain of each node. Because there are cracks in the structure, when determining the support domain, it is defined that the nodes on one side of the crack will not appear in the support domain of the nodes on the other side. Such as Figure 11 As shown, node P 1 does not contain P in the support domain 5 , node P 5 does not contain P in the support domain 1 .
[0131] At the same time, the boundary that coincides with the crack is set as a free boundary. Such as Figure 11 As shown, the boundary Γ 26 , Γ 15 and Γ 47 for the free boundary.
[0132] Step C23: Calculate the expression u of the test function in each subdomain using the weighted least squares method h = Nu E , N is the shape function, u E is the node displacement.
[0133] Test...
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Abstract
The invention discloses a meshless solid mechanical simulation method. The method comprises the following steps: firstly, constructing a test function and a test function through point distribution according to the structural geometrical shape of an object; and then introducing numerical flux to obtain a Galerkin weak form with numerical flux correction, finally substituting a test function and atest function into the weak form to establish a structure overall rigidity matrix and an algebraic equation set, and solving the equation set to obtain displacement and stress of each node, thereby completing deformation and stress simulation analysis of the structure. Structural simulation is achieved by providing a discontinuous test function, a discontinuous check function and a corresponding weak form, the calculation efficiency and the simulation precision are improved, and the problem that a traditional simulation method is difficult to carry out extreme problem simulation such as fracture and breakage is solved. The invention further provides electronic equipment and a storage medium.
Description
technical field [0001] The invention relates to a mechanical simulation system, in particular to a gridless solid mechanical simulation method, electronic equipment and a storage medium. Background technique [0002] Structural stress analysis is very important and necessary in different engineering fields such as aviation, aerospace, and automobile. Structural stress analysis plays a vital role in product design, manufacture and maintenance. Because of its importance, many researchers have been working for decades to improve the accuracy and efficiency of this process. [0003] At present, the finite element method (Finite Element Method) is widely used in structural stress analysis. The method uses element-based, local, polynomial, continuous test and inspection functions for simulation. Since the test and inspection functions are polynomial, integrals in the finite element method are easy to compute, and the symmetry and sparsity of the overall stiffness matrix make th...
Claims
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