The Trefftz Finite and Boundary Element Method

TLDR: In this paper, the concept of T-complete solution is used to compare T-elements with conventional finite elements with boundary elements, and a variational formulation for thin plate bending is proposed.

Abstract: Part 1: finite element technique shape functions and element stiffness matrix brief historical background basic relationships in engineering problems modified variational principles the concept of T-complete solution comparison of T-elements with conventional finite elements comparison of T-elements with boundary elements. Part 2: potential problems - introduction statement of the problem T-complete functions assumed fields generation of element matrix equation rank condition special purpose functions sensitivity to mesh distortion orthotropic case the Helmholtz equation HT-element with boundary "traction" frame frameless T-elements. Part 3: linear elastostatics - introduction linear theory of elasticity assumed fields in plane elasticity T-complete functions variational formulations element stiffness equation special-purpose elements p-extension approach three-dimensional elasticity numerical examples. Part 4: thin plates - introduction thin plate theory assumed field T-complete functions and particular solutions variational formulations for plate bending generation of element stiffness matrix p-method elements special purpose functions Extension to thin plates on elastic foundation Two alternative plate bending p-elements Numerical examples and assessment. Chapter 5 - Thick Plates - Introduction Basic equations for Reissner-Mindlin plate theory Assumed fields and particular solution Variational formulation for HT thick plate elements Implementation of the new family of HT elements A 12 DOF quadrilateral element free of shear locking Extension to thick plates on elastic foundation Sensitivity to mesh distortion Numerical assessment. Chapter 6 - Transient Heat Conduction - Introduction Elements of heat conduction Time step formula Element matrix formulations T-complete functions and particular solutions Numerical examples. Chapter 7 - Geometrically Nonlinear Analysis of Plate Bending Problems - Introduction Basic equations of nonlinear thin plate bending Assumed fields and Trefftz functions Particular solutions Modified variational principle Element matrix Iterative scheme Extension to post-buckling thin plates on elastic foundation Geometrically nonlinear analysis of thick plates Numerical examples. Chapter 8 - Elastoplasticity - Introduction Time discretization Basic relations Assumed fields Constraints on the approximation functions Finite element equilibrium and compatibility equations Finite element equations Finite element governing system. Chapter 9 - Dynamics of Plate Bending Problems - Introduction Basic equations Time-stepping formulation Numerical examples. Chapter 10 - Trefftz Boundary Element Method - Introduction Potential problems Plane elasticity Thin plate bending Moderately thick plates.