Elastostatic and elastodynamic analysis of structures with p-version finite elements

The purpose of this study is to develop p-version finite element program (pFEM) augmented by blending function method with which application of continuous or discontinuous nonlinear load, elastostatic and elastodynamic analysis, exactly representation of curved edge and/or surface boundary are performed with degree of freedoms (DOFs) through translations in orthogonal three direction. For this purpose, Lagrange, Lagrange polynomial based hierarchic, Legendre polynomial based hierarchic, Lagrange polynomial based serendipity, serendipity formed hierarchic Lagrange, serendipity formed hierarchic Legendre, body DOFs reduced Lagrange finite element that have different interpolation property are taken into consideration. The last three finite elements are introduced to reduce the number of DOFs in the concept of this thesis.This study consists of four chapters. In the first chapter, after a brief literature review about finite element method and high order finite element method types, general forms of the constructed interpolation functions are given. After graphical examination of displacement field is conducted, literature review about blending function and its general form is prescribed, and then the purpose and scope of this study are presented. In the second chapter, construction of mass, stiffness and load matrices according to pFEM, numbering of DOFs in the existing mesh occurred because of increasing polynomial degree, representation of circle-curved edge and/or surface within blending function method, nonlinear loading is presented. In the third chapter, after verification of the developed program on mechanical examples at the elastostatic analysis and getting general impression, elastostatic and elastodynamic analysis are performed in industrial chimney collapsed on August 17, 1999 under uniformly distributed load according to TS 498 and under nonlinear distributed load according to TS 498 and prEN 1991-1-4. In the fourth chapter, the conclusions drawn from the results are presented and recommendations are made. This chapter is followed by a list of references.It is concluded that the developed p-version finite element program gives reliable result and the given types of finite element in this study can be effectively used.