BF-spline Ritz法を用いた固定辺と自由辺を有する長方形厚板の曲げ解析

抄録

This paper presents a numerical method, the BF-spline Ritz method, for bending analysis of rectangular Mindlin plates with clamped and free edges. The proposed method utilizes admissible functions comprising the B-spline functions multiplied by a boundary function to define the Ritz trial function for the transverse displacement and rotations of the Mindlin plates. The geometric boundary conditions of the plate at edges are automatically satisfied using boundary functions. To demonstrate the validity and accuracy of the BF-spline Ritz method, several examples are solved, and results are compared with those obtained by analytical and other numerical methods. Good convergence and accuracy are obtained by the present method. The effects of Poisson’s ratio, thickness-width ratio and aspect on the distributions of deflections, bending moments and shear forces of rectangular Mindlin plates due to distributed load are shown. The results obtained are to serve as benchmark data for future development of new numerical methods.