モード重ね合せ法におけるUpdated-Lagrange 定式化の適用について : その1.薄肉弾性体の軸対称大変形解析

抄録

In this paper, the updated-lagrangian formulation which is usually used in the finite element method with considering the reference convected local co-ordinate system, is applied to the Mode Superposition Method by refering to the convected curvilinear co-ordinate system. In this formulation, the strain-displacement transformation matrices do not contain the initial strain components, and the transformation matrices of co-ordinates become successively variable values in the continuum. All components in the strain-displacement matrices and all components in the transformation matrices of co-ordinates change as the continuum deforms. Here, the change of the components is estimated with the change of the metric tensor, etc. in the convected curvilinear co-ordinate system and the direction cosines of angles formed between the global co-ordinate system and the local co-ordinate system on the points of the numerical integration at each step routine or each iteration routine. The present results for some examples point out that total-lagrangian formulation refered to the initial configuration come to have errors in the very large deformation region of post-buckling, and the present method using the updated-lagrangian formulation can follow the behaviour in that region.