Analysis and Optimization of Prismatic and Axisymmetric Shell Structures: Theory, Practice and Software - Couverture souple
Synopsis
I: Introduction.- 1 Introduction.- 1.1 Background.- 1.2 Previous work.- 1.2.1 Structural shape optimization of shells and folded plates under static conditions.- 1.2.2 Vibrating shells of revolution.- 1.2.3 Vibrating prismatic shells and folded plates.- 1.3 Classification of structural optimization problems.- 1.3.1 Classification based on mode of behaviour.- 1.3.2 Classification according to type of design variable.- 1.4 Classification of shells.- 1.4.1 Indian Standard classification of shells and folded plates.- 1.4.2 Simplified classification of shells and folded plates.- 1.4.3 Summary of structures considered.- 1.5 Computer-aided shape definition.- 1.5.1 Shape definition of shells of revolution and prismatic shells.- 1.6 Element technology.- 1.6.1 Elements for shells of revolution.- 1.6.2 Strips for prismatic shells.- 1.7 Automatic mesh generation.- 1.7.1 Automatic mesh generation for shells of revolution and prismatic shells.- 1.8 Structural shape optimization.- 1.8.1 The basic algorithm.- 1.8.2 Sensitivity analysis.- 1.8.3 Sensitivity analysis of static response.- 1.8.4 Sensitivity analysis of dynamic problems.- 1.8.5 Selection and linking of design variables.- 1.8.6 Selection of constraint points.- 1.8.7 Optimization algorithm.- 1.9 Typical shell problems treated.- 1.10 Software developed in this book.- 1.11 Layout of the book.- References.- 2 Structural Shape Definition and Automatic Mesh Generation with contributions from NVR Rao.- 2.1 General perspective.- 2.2 Structural shape definition.- 2.2.1 Three equivalent representations of a parametric cubic spline.- 2.2.2 The cubic B-spline representation.- 2.2.3 Terminology.- 2.2.4 Computer implementation.- 2.2.5 Specification of end condition of splines.- 2.3 Structural thickness definition.- 2.4 Automatic mesh generation.- 2.4.1 General requirements.- 2.4.2 Algorithm for mesh generation.- 2.5 Shape definition and mesh generation in structural analysis.- 2.6 Shape definition and mesh generation in structural optimization.- 2.6.1 Shape design variables.- 2.6.2 Selection of thickness design variables.- 2.6.3 Linking of design variables.- 2.6.4 Perturbation of design variables.- 2.6.5 Prescribed move directions.- 2.7 Other applications of the present tools.- References.- 3 Structural Optimization Methods and Algorithms.- 3.1 General perspective.- 3.1.1 Problem classification.- 3.1.2 Problem definition and formulation.- 3.1.3 Basic algorithm and three-columns concept.- 3.1.4 Other important aspects.- 3.2 Optimization algorithms.- 3.2.1 Overview.- 3.2.2 Mathematical programming.- 3.2.3 Genetic algorithms.- 3.2.4 Approximation concepts.- 3.3 Sensitivity analysis.- 3.3.1 Overview.- 3.3.2 Global finite differences.- 3.3.3 Semi-analytical method.- 3.3.4 Analytical or direct sensitivity method.- 3.3.5 Adjoint variable method.- 3.3.6 Accuracy assessment.- 3.4 Concluding remarks.- References.- II: Static Analysis and Optimization.- 4 Basic Finite Element Formulation for Shells of Revolution.- 4.1 General perspective.- 4.2 Basic formulation.- 4.3 Finite element idealization.- 4.4 Strain energy evaluation.- 4.5 Benchmark examples.- 4.5.1 Cylindrical tank with non-uniform wall thickness.- 4.5.2 Clamped circular plate.- 4.5.3 Spherical dome under uniform pressure.- 4.5.4 Toroidal shell under internal pressure.- 4.6 Closing remarks.- References.- 5 Basic Finite Strip Formulation for Prismatic Shells with contributions from NVR Rao.- 5.1 General perspective.- 5.1.1 Preamble.- 5.1.2 Simply supported Euler-Bernoulli beam.- 5.1.3 Simply supported Timoshenko beam.- 5.2 Right prismatic shells.- 5.2.1 Basic formulation.- 5.2.2 Finite strip idealization.- 5.2.3 Branched strips.- 5.3 Benchmark examples.- 5.3.1 Plates.- 5.3.2 Box-girder bridges.- 5.3.3 Cylindrical shells.- 5.4 Prismatic structures with curved planform.- 5.4.1 Basic formulation.- 5.4.2 Branched strips.- 5.5 Benchmark examples.- 5.5.1 Comparisons with known solutions for right structures analyzed as structures with curved planform.- 5.
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