The Trefftz Finite and Boundary Element Method

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.