Finite Block Method in elasticity
A new point collocation algorithm named Finite Block Method (FBM), which is based on the one-dimensional differential matrix is developed for 2D and 3D elasticity problems in this paper. The main idea is to construct the first order one-dimensional differential matrix for one block by using Lagrange series with uniformly distributed nodes. The higher order derivative matrix for one-dimensional problem is obtained. By introducing the mapping technique, a block of quadratic type is transformed from Cartesian coordinate(xyz) ( x y z ) to normalised coordinate (???) ( ? ? ? ) with 8 seeds or 20 seeds for two or three dimensions. The differential matrices in physical domain are determined from that in the normalised transformed system. Several 2D and 3D examples are given and comparisons have been made with either analytical solutions or the boundary element method to demonstrate the accuracy and convergence of this method.
finite block method elasticity 1d mapping differential matrix lagrange series expansion functionally graded media anisotropy