Elastic large deflection of circular plates using graded finite-differences

Abstract

Axisymmetric elastic large deflection circular plate analysis is briefly reviewed and the apparent popularity of uniform mesh finite-difference numerical solution techniques is noted. The inherent limitations of uniform meshes, especially the inability to accommodate local refinement, are discussed. The use of graded interlacing meshes is advanced as a more flexible alternative to uniform meshes and a description of a Dynamic Relaxation (DR) large deflection graded mesh circular plate analysis is presented in detail. The accuracy of several graded mesh solutions, compared with corresponding uniform mesh results, is explored via the large deflection analysis of uniformly loaded clamped and simply supported circular plates and similar plates with an interior concentric support. In general, it is established that deflections and stress couples are computed more accurately and stress resultants less accurately with graded meshes. The use of gradually graded meshes leads to the most consistently accurate results.