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Nonlinear mechanics of structures

Author: Michał Kleiber; Czesław Woźniak
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers ; Warsaw : PWN--Polish Scientific Publishers, ©1991.
Series: Mechanics of structural systems, 8.
Edition/Format:   Print book : EnglishView all editions and formats
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The aim of this book is to provide a unified presentation of modern mechanics of structures in a form which is suitable for graduate students as well as for engineers and scientists working in the  Read more...

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Document Type: Book
All Authors / Contributors: Michał Kleiber; Czesław Woźniak
ISBN: 0792307208 9780792307204
OCLC Number: 21227656
Notes: Translation of: Nieliniowa mechanika konstrukcji.
Description: xv, 458 pages : illustrations ; 25 cm.
Contents: I: Theoritical Foundations.- 1 General notions and principles.- Purpose of the chapter.- 1.1 Introductory concepts.- 1.1.1 Space and time.- 1.1.2 Motion.- 1.1.3 Mass.- 1.1.4 Forces.- 1.1.5 Temperature, energy and entropy.- 1.1.6 Heat supply.- 1.2 Fundamental principles.- 1.2.1 Balance of momentum.- 1.2.2 Balance of moment of momentum.- 1.2.3 Balance of energy.- 1.2.4 Dissipation principle.- 1.3 Basic fields.- 1.3.1 Displacements.- 1.3.2 Strains and strain rates.- 1.3.3 Stresses and stress rates.- 1.3.4 Heat fluxes.- 1.3.5 Matrix notation for the basic fields.- 1.4 Resulting relations.- 1.4.1 Equation of motion.- 1.4.2 Energy equation.- 1.4.3 Dissipation inequality.- 1.4.4 Matrix form of the resulting equations.- Summary.- Problems.- 2 Materials, loadings and constraints.- Purpose of the chapter.- 2.1 Materials.- 2.1.1 Real materials and ideal materials.- 2.1.2 Thermo-visco-elastic materials.- 2.1.3 Linear thermo-elastic materials.- 2.1.4 Thermo-elastic-plastic materials.- 2.1.5 Matrix form of constitutive relations.- 2.2 Loadings and heat supply.- 2.2.1 External agents.- 2.2.2 Body loadings and internal heat supply.- 2.2.3 Boundary loadings.- 2.2.4 Boundary heat supply.- 2.3 Constraints.- 2.3.1 Boundary and internal constraints.- 2.3.2 Reactions.- 2.3.3 Bilateral constraints.- 2.3.4 Constraint functions.- 2.3.5 Constraints for stresses and heat fluxes.- Summary.- Problems.- 3 Formulation of engineering theories.- Purpose of the chapter.- 3.1 General form of governing relations.- 3.1.1 Finite variational formulation.- 3.1.2 Incremental variational formulation.- 3.1.3 Variational equations for stresses and heat fluxes.- 3.1.4 Calculation of reactions.- 3.1.5 Matrix form of variational equations.- 3.2 Method of constraints: finite formulation.- 3.2.1 Foundations.- 3.2.2 Shell and plate theories.- 3.2.3 Rod and beam theories.- 3.2.4 Plane problems.- 3.3 Method of constraints: incremental formulation.- 3.3.1 General equations.- 3.3.2 Shells and rods.- 3.3.3 Plane problems.- 3.4 Method of constraints: discrete description of elements and structures.- 3.4.1 Discretization concept.- 3.4.2 Finite formulation.- 3.4.3 Incremental formulation.- 3.4.4 Shell and plate elements.- 3.4.5 Rod and beam elements.- 3.4.6 Special cases and matrix notation.- 3.4.7 Interaction between elements.- 3.5 Evaluation and correction of solutions.- 3.5.1 Residual reactions.- 3.5.2 Evaluation of solutions.- 3.5.3 Correction of solutions.- 3.5.4 On adaptive solution refinements.- Summary.- Problems.- 4 Extensions and specifications of the general theory.- Purpose of the chapter.- 4.1 Domain discretization.- 4.2 Solving differential equations by weighted residual methods.- 4.3 Assembly of element matrices and vectors.- 4.4 Elastic pin-jointed element in space.- 4.5 Elastic frame element in space.- 4.6 Elastic lattice-type structures.- 4.6.1 Discrete models.- 4.6.2 Continuous models.- 4.7 Engineering shell theories.- 4.7.1 Foundations.- 4.7.2 General form of equations of motion.- 4.7.3 Special theories.- 4.7.4 Example: axisymmetric deformations of shells.- 4.8 Thin shell finite element for nonlinear axisymmetric analysis.- 4.9 Linear strain triangular element for nonlinear plane stress analysis.- 4.10 Constitutive matrices for thermo-elastic-plastic materials.- 4.11 On inelastic analysis under non-proportionally varying loads..- 4.11.1 Elastic-plastic structures subjected to mechanical loads..- 4.11.2 Thermo-elastic-plastic structures subjected to mechanical and thermal loads.- Summary.- Problems.- 5 Numerical algorithms and software concepts.- Purpose of the chapter.- 5.1 Introductory comments.- 5.2 Nonlinear quasi-statics.- 5.3 Integration of elastic-plastic constitutive law.- 5.4 Initial and linearized buckling.- 5.5 Nonlinear dynamics.- 5.6 Dynamic stability under non-periodic loads.- 5.7 Nonlinear heat transfer.- 5.8 Development of software.- Summary.- Problems.- II: SELECTED APPLICATIONS.- 6 Trusses, frames, lattice-type shells.- Purpose of the chapter.- 6.1 Trusses.- 6.1.1 Nonlinear effects in truss analysis - a model problem.- 6.1.2 Accuracy of computations and further examples.- 6.1.3 Elastic-plastic truss under non-proportionally varying loads.- 6.2 Frames.- 6.2.1 Elastic-plastic constitutive matrices for beam elements.- 6.2.2 Limit state conditions.- 6.2.3 Nonlinear analysis of curved beams.- 6.2.4 Examples of numerical frame analysis up to collapse.- 6.2.5 Elastic-plastic beam under non-proportionally varying loads..- 6.2.6 Elastic buckling of plane grid.- 6.2.7 Approximate large displacement analysis of frames using buckling mode superposition.- 6.3 Lattice-type structures.- 6.3.1 Lattice shells - linear and "second-order" theories.- 6.3.2 Buckling of elastic grid.- 6.3.3 Perfectly-plastic lattice-type plates - discrete model.- 6.3.4 Limit load of polar grids - continuous model.- 6.3.5 Minimum weight design of ideally plastic rectangular dense grid.- Summary.- Problems.- 7 Thin plates loaded in-plane.- Purpose of the chapter.- 7.1. Elastic-plastic bending of a cantilever beam.- 7.2 Limit analysis of perforated plates.- 7.3 Elastic-plastic analysis of a cantilever under non-proportionally varying loads.- 7.4 In-plane buckling of an elastic-plastic strip.- 7.5 Necking of an elastic-plastic strip.- 7.6 Extension of a thin rectangular plate with a central hole.- Summary.- 8 Plate and shell problems..- Purpose of the chapter.- 8.1 Thin elastic-plastic axisymmetric shells.- 8.2 Elastic-viscoplastic analysis of axisymmetric shells.- 8.3 Buckling of elastic-plastic spatial plate assemblies.- Summary.- 9 Heat conduction and thermal stress problems.- Purpose of the chapter.- 9.1 Heat flow in flash and friction welding.- 9.2 Thermally induced stresses in elastic-plastic plate.- 9.3 Elastic-plastic cylindrical shell under thermo-mechanical load..- 9.4 Elastic-plastic truss under nonproportionally varying temperature and mechanical load.- Summary.
Series Title: Mechanics of structural systems, 8.
Other Titles: Nieliniowa mechanika konstrukcji.
Responsibility: Michał Kleiber and Czesław Woźniak.
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