Suchergebnisse

1 Fundamentals of the Finite Element Method -- 1.1 Introduction -- 1.2 The concept of discretization -- 1.3 Steps in the finite element method -- References -- 2 Finite Element Analysis in Heat Conduction -- 2.1 Introduction -- 2.2 Review of basic formulations -- 2.3 Finite element formulation of transient heat conduction in solids -- 2.4 Transient heat conduction in axisymmetric solids -- 2.5 Computation of the thermal conductivity matrix -- 2.6 Computation of the heat capacitance matrix -- 2.7 Computation of thermal force matrix -- 2.8 Transient heat conduction in the time domain -- 2.9 Boundary conditions 45 2.10 Solution procedures for axisymmetric structures -- References -- 3 Thermoelastic-Plastic Stress Analysis -- 3.1 Introduction -- 3.2 Mechanical behavior of materials -- 3.3 Review of basic formulations in linear elasticity theory -- 3.4 Basic formulations in nonlinear elasticity -- 3.5 Elements of plasticity theory -- 3.6 Strain hardening -- 3.7 Plastic potential (yield) function -- 3.8 Prandtl-Reuss relation -- 3.9 Derivation of plastic stress-strain relations -- 3.10 Constitutive equations for thermoelastic-plastic stress analysis -- 3.11 Derivation of the [Cep] matrix -- 3.12 Determination of material stiffness (H') -- 3.13 Thermoelastic-plastic stress analysis with kinematic hardening rule -- 3.14 Finite element formulation of thermoelastic-plastic stress analysis -- 3.15 Finite element formulation for the base TEPSAC code -- 3.16 Solution procedure for the base TEPSA code -- References -- 4 Creep Deformation of Solids by Finite Element Analysis -- 4.1 Introduction -- 4.2 Theoretical background -- 4.3 Constitutive equations for thermoelastic-plastic creep stress analysis -- 4.4 Finite element formulation of thermoelastic-plastic creep stress analysis -- 4.5 Integration schemes -- 4.6 Solution algorithm -- 4.7 Code verification -- 4.8 Closing remarks -- References -- 5 Elastic-Plastic stress analysis with Fourier Series -- 5.1 Introduction -- 5.2 Element equation for elastic axisymmetric solids subject to nonaxisymmetric loadings -- 5.3 Stiffness matrix for elastic solids subject to nonaxisymmetric loadings -- 5.4 Elastic-plastic stress analysis of axisymmetric solids subject to nonaxisymmetric loadings -- 5.5 Derivation of element equation -- 5.6 Mode mixing stiffness equations -- 5.7 Circumferential integration scheme -- 5.8 Numerical example -- 5.9 Discussion of the numerical example -- 5.10 Summary -- References -- 6 Elastodynamic stress analysis with Thermal Effects -- 6.1 Introduction -- 6.2 Theoretical background -- 6.3 Hamilton's variational principle -- 6.4 Finite element formulation -- 6.5 Direct time integration scheme -- 6.6 Solution algorithm -- 6.7 Numerical illustration -- References -- 7 Thermofracture Mechanics -- 1: Review of fracture mechanics concept -- 2: Thermoelastic-plastic fracture analysis page -- 3: Thermoelastic-plastic creep fracture analysis -- References -- 8 Thermoelastic-Plastic Stress Analysis By Finite Strain Theory -- 8.1 Introduction -- 8.2 Lagrangian and Eulerian coordinate systems -- 8.3 Green and Almansi strain tensors -- 8.4 Lagrangian and Kirchhoff stress tensors -- 8.5 Equilibrium in the large -- 8.6 Equilibrium in the small -- 8.7 The boundary conditions -- 8.8 The constitutive equation -- 8.9 Equations of equilibrium by the principle of virtual work -- 8.10 Finite element formulation -- 8.11 Stiffness matrix [K2] -- 8.12 Stiffness matrix [K3] -- 8.13 Constitutive equations for thermoelastic-plastic stress analysis -- 8.14 The finite element formulation -- 8.15 The computer program -- 8.16 Numerical examples -- References -- 9 Coupled Thermoelastic-Plastic Stress Analysis -- 9.1 Introduction -- 9.2 The energy balance concept -- 9.3 Derivation of the coupled heat conduction equation -- 9.4 Coupled thermoelastic-plastic stress analysis -- 9.5 Finite element formulation -- 9.6 The y matrix -- 9.7 The thermal moduli matrix ? -- 9.8 The internal dissipation factor -- 9.9 Computation algorithm -- 9.10 Numerical illustration -- 9.11 Concluding remarks -- References -- 10 Application of Thermomechanical Analyses in Industry -- 10.1 Introduction -- 10.2 Thermal analysis involving phase change -- 10.3 Thermoelastic-plastic stress analysis -- 10.4 Thermoelastic-plastic stress analysis by TEPSAC code -- 10.5 Simulation of thermomechanical behavior of nuclear reactor fuel elements -- References -- Appendix 1 Area coordinate system for triangular simplex elements -- Appendix 2 Numerical illustration on the implementation of thermal boundary conditions -- Appendix 3 Integrands of the mode-mixing stiffness matrix -- Appendix 4 User's guide for TEPSAC -- Appendix 5 Listing of TEPSAC code -- Author Index.

"This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution. The book gives an excellent insight in the present ideas and methods of analysis."--Jacket

The efficient codes can take an advantage of multiple threads and/or processing nodes to partition a work that can be processed concurrently. This can reduce the overall run-time or make the solution of a large problem feasible. This paper deals with evaluation of different parallelization strategies of assembly operations for global vectors and matrices, which are one of the critical operations in any finite element software. Different assembly strategies for systems with a shared memory model are proposed and evaluated, using Open Multi-Processing (OpenMP), Portable Operating System Interface (POSIX), and C++11 Threads. The considered strategies are based on simple synchronization directives, various block locking algorithms and, finally, on smart locking free processing based on a colouring algorithm. The different strategies were implemented in a free finite element code with object-oriented architecture OOFEM [1].

Digital Terrain Modeling (DTM) is a computational model of the earth surface that represents relief and it has a wide range of applications. This work proposes a new approach to DTM using the Finite Element Method (FEM) point-based instead of mesh-based. The points used by the proposed methodology were obtained by data captured by satellite images. The most methods require the precomputation of a mesh on the surface of the terrain. Our methodology overcomes the mesh step, so the modeling process is very fast.