非線形計画法による平板の大たわみ解析 : 第1報, 面外変位の非線形項を考慮した軸対称問題

抄録

This paper investigates the methodology of the large deflection analysis of the axisymmetric problem using the nonlinear programming theory. In the strain-displacement relationship, the out-of-plane displacement is assumed to be the nonlinear term. The total potential energy is expressed by the regular quadratic, cubic, and quartic terms. The cubic energy element indicates the coupling term between the out-of-plane and in-plane displacements. The exact total potential energy is directly minimized by the Davidon-Fletcher-Powell method. The numerical examples of a rigidly clamped annular plate subjected to the compressive load are shown. The maximum deflection and the stress distribution of the annular plates are given in the case of the coupling and noncoupling theories. The results obtained by this method are compared with the previous solutions. It is concluded that the large deflection in the plate bending can be analyzed by this method in a single loading without using load increments.