An approach for verification of finite-element analysis in nonlinear elasticity under large strains

11th International Conference on "Mesh methods for boundary-value problems and applications"

Zingerman, K.M.^1 ; Vershinin, A.V.^2 ; Levin, V.A.^3

Tver State University, 33 Zhelyabov Street, Tver

170100, Russia^1

Fidesys LLC, MSU Science Park, Leninskie Gory, Moscow

119234, Russia^2

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Main Building, 1 Leninskiye Gory, Moscow

119991, Russia^3

关键词: Compressible hyperelastic materials;    Exact analytical solutions;    Nonlinear elastic bodies;    Nonlinear elasticity;    Numerical solution;    Second order nonlinear differential equation;    Semi inverse methods;    Stress strain state;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012104/pdf
DOI  :  10.1088/1757-899X/158/1/012104

来源: IOP

【 摘 要 】

An approach to verification of finite-element calculations of stress-strain state of nonlinear elastic bodies under large deformations is suggested. The problems that may be reduced to one-dimensional ones using a semi-inverse method are taken as test problems. An example of such a test problem is the Lame problem for a cylinder. Generally, this problem for compressible hyperelastic materials has no exact analytical solution, but it can be reduced to a boundary value problem for an ordinary second-order nonlinear differential equation, and in some cases - to the Cauchy problem. A numerical solution of this problem can be used as a test one for finite element calculations carried out in three-dimensional statement. Some results of such verification (finite element calculations were performed using the Fidesys CAE-system) are presented.