Bott・Duffin逆行列による変位制限を持つ構造物の解析

抄録

This paper deals with the structural ayalysis, in the linear and the geometrically nonlinear regions, of structures with constraint conditions of displacement. First, the total potential energy function with subsidiary conditions which express the inequality conditions of some displacement components is introduced, and then the following constrained system is derived by minimizing the total potential energy function, based on the Lagrange multiplier method for the constraint condition Ku+r=f………(1) where K: stiffness matrix in the incremental interval, u: incremental displacement, r: incremental reaction, f incremental load. First, the orthogonal condition of u and r is proved by means of the constraint condition. Then, the Bott・Duffin inverse can be effectively used for analyzing Eq. (1), and incremental displacements as well as reaction of nodes which is contact with a rigid body are numerically obtained from Eq. (1). In the paper, the derivation of basic equations, a brief introduction of Bott・Duffin inverse, the numerical method, and some illustrative examples are presented.