Convergence Analysis Of Coupled Equations In The Non-newtonian Fluid

At present the car crash tests mainly analyze the corresponding models by computertechnology and finite element analysis method. This paper uses fluid-structure coupledequations (Cauchy equation and P-T/T equation), which describes the material propertiesof visco-elastic plastic on a macroscopic scale.Cauchy equation describe the deformationof the stress field, P-T/T equation describes the stress of the stress field. The coupledequations are simulated non-Newtonian phenomenon of the visco-elastic plastic material.It researches velocity field and stress field from collision model by high-performancecomputing software(OASYS-PRIMER and LS-DYNA) on a microscopic scale.The paperstudies the convergence of coupled equations which based on the Sobolev theory andsemi-discrete finite element method.Firstly, the coupled equations are discreted with Lagrange finite element methodand then we get nonlinear equations. Due to the symmetry of the Cauchy equation expan-sion, one of which is only studied.In space we get the weak solution of Cauchy equationusing variational method.Through cut operator of the nonlinear equations,its convergenceis proved. In terms of time Euler backward diference scheme is used,then semi-discretefinite element solution of Cauchy equations can reach a certain precision.Secondly, it takes advantage of three linear functional because of its nonlinear.It studies the convergence of coupled equations by semi-discrete finite element methodwhich uses Euler backward diference scheme in time and Lagrange shape function inspace. The coupled equations reach a certain precision under appropriate step and fixedparameters. The meshes on the contact surface make great changes under inappropriatestep. In addition, under the same conditions, C-N format is more superior and betterconvergence than Euler.Finally, with the help of high-performance computing platform, it analyses the col-lision speed and the contact surface element stress which is dealt with three-dimensionalsimulation.