Abstract
A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.
Abstract
Although various analytical and numerical methods have been proposed by researchers to solve equations, but use of numerical tools with low volume calculations and high accuracy instead of other numerical methods with high volume calculations is inevitable in the analysis of engineering equations. In this paper, B-Spline spectral method was used to study buckling equations of the piles. Results were compared with the calculated amounts of the exact solution and finite element method. Uniform horizontal reaction coefficient has been used in most of proposed methods for analyzing buckling of the pile on elastic base. In reality, soil horizontal reaction coefficient is nonlinear along the pile. So, in this research by using B-Spline method, buckling equation of the pile with nonlinear horizontal reaction coefficient of the soil was investigated. It is worth mentioning that B-Spline method had not been used for buckling of the pile.
Evaluation of Pile’s Buckling Under Axial Load by B-Spline Method and Comparison With Finite Element Method and Exact Solution
