Application of point least squares method with B‐splines in solid mechanics problems

Abstract

SUMMARYA discrete approach using the B-spline functions and the concept of the point least square is presented.The general procedure, in which trial functions satisfy neither governing differential equations nor boundary conditions, is used in solving solid mechanics problems. No numerical integration is required in the formulation and the resulting matrix has the advantage of always being symmetrical.To demonstrate the accuracy and versatility of the present method, vibration of beams, skew plate problems, thick plates and a non-self-adjoint problem are analysed. A good accuracy is obtained with increase in the number of fitting points and of knots of B-spline functions.

Discrete least‐squares global approximations to solutions of partial differential equations

“…Yet the trend in the last decade has been towards finite elements, where least-square functions were frequently fitted on each element [2,3].…”

“…As early as 1976, Eason [l] compiled tables of papers related to the solution of partial differential equations (PDEs) using least-square methods. Yet the trend in the last decade has been towards finite elements, where least-square functions were frequently fitted on each element [2,3].…”