The Modelling of Nonlinear Mechanics Problems Using Spline Functions

109 leaves : illustrations.This thesis proposes a method of solving nonlinear mechanics problems using parametric or non-parametric cubic splines. A wide variety of mechanics problems lead to initial and/or boundary-value problems. By the introduction of splines, the foregoing problems can be formulated as algebraic ones, their solutions thus reducing to those of a nonlinear algebraic system. This method allows the problem to be formulated as a nonlinear overdetermined system of algebraic equations, which is then solved by the Newton-Gauss method, which assures monotonical convergence. The use of continuation further speeds convergence. The method proposed here is illustrated by two problems of practical importance in a variety of mechanical engineering applications