Based On S-R Decomposition Theorem Analysis Of Element Free Galerkin Method On Geometric Nonlinear Problems

Generally, large displacement and large rotation are features of geometricnonlinear problems. When we establish the balance equation on object or infinitesimalbody, the change of location and configuration must be considered, and on the processof shape change, strain can’t be measured by linear strain of the first derivative ofdisplacement. In order to establish balance equation, reasonable strain measuremethod should be used. The research of geometric nonlinear problems is full ofimportant significance in structural analysis.The S-R decomposition theorem divides movement transformation into rotationtransformation and deformation transformation by mathematical methods,deformation tensor is used to measure strain, which overcome the problem of Greenstain tensor on the local rotation uncertainty. So, deformation tensor is a reasonablemeasure method on stain.First, based on the strain tensor under S-R decomposition theorem, incrementalvariation equation is derived from fictitious power principle, which is used toincremental analysis in updated co-moving coordinate. Derivative functions areresearched on each physical quantity in co-moving coordinate, and the objective ofstress rate which isn’t effected by rigid bode rotation is proved. So stress rate could beapplied in the rate model of constitutive equation.Second, considering incremental variation equation as global variation weakform, base on shape function constructed by the moving least square, discrete systemequation is deduced for element free Galerkin method. Because of system equationrelating to displacement, it is nonlinear. The Newton-Raphson method, owing goodconvergence, is used to interactively solve system equation. The way to calculatestrain increment and stress increment is discussed.Last, several geometrical nonlinear problems are solved by element free Galerkinmethod, which contain elastic geometrical nonlinear problem, elastic-plasticgeometrical nonlinear problem and including hole geometrical nonlinear problem.Examples show that based on S-R decomposition theorem element free Galerkinmethod has good convergence and accuracy.