| Chapter 1 |
Introduction |
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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. |
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| Chapter 2 |
Potential Problems |
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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. |
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| Chapter 3 |
Linear Elastostatics |
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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. |
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| Chapter 4 |
Thin Plates |
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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. |
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| Chapter 5 |
Thick Plates |
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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. |
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| Chapter 6 |
Transient Heat Conduction |
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Introduction; Elements of heat conduction;
Time step formula; Element matrix formulations; T-complete functions and
particular solutions; Numerical examples. |
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| Chapter 7 |
Geometrically Nonlinear Analysis of Plate
Bending Problems |
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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. |
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| 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. |
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| Chapter 9 |
Dynamics of Plate Bending Problems |
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Introduction; Basic equations; Time-stepping
formulation; Numerical examples. |
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| Chapter 10 |
Trefftz Boundary Element Method |
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Introduction; Potential problems;
Plane elasticity; Thin plate bending; Moderately thick plates. |