Numerical test for the Neumann problem of interior BVP of plane elasticity

摘要

Following the concept of the patch test in FEM (finite element method), several numerical tests are suggested for the Neumann problem of interior BVP (boundary value problem) of plane elasticity by using different techniques. We choose the elliptic plate as an object in the test. Along the boundary of the plate, two groups of boundary traction are assumed. The first group is derived from the constant stress solution (or constant strain solution), and the second group is derived from the linear stress distribution. From displacement solution, we can evaluate the normal peripheral stress along the boundary, which is compared with the result from an exact solution. In addition, several error estimation factors are defined to evaluate the achieved accuracy. Extensive numerical examples and computed results are provided.