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A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function(RBF)coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.
A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material. In the present method, a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function (RBF) coupled with a polynomial basis function, in which the shape function possesses the kronecker delta function property. So, additional treatment is not required for imposing essential boundary conditions. Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain, which is very similar to that of the colliding method except that numerical integration can be implemented over local domain in the present method. Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.