Ebook: Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells: Applications of the Bubnov-Galerkin and Finite Difference Numerical Methods

This monograph, addressing researchers as well as engineers, is devoted to nonclassical thermoelastic modelling of the nonlinear dynamics of shells. Differential equations of different dimensionality and different type have to be combined and nonlinearities of different geometrical, physical or elasto-plastic categories are addressed. Special emphasis is given to the Bubnov--Galerkin method. It can be applied to many problems in the theory of plates and shells, even those with very complex geometries, holes and various boundary conditions. The authors made every effort to keep the text intelligible for both practitioners and graduate students, although they offer a rigorous treatment of both purely mathematical and numerical approaches presented so that the reader can understand, analyse and track the nonlinear dynamics of spatial systems (shells) with thermomechanical behaviours.

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This monograph, addressing researchers as well as engineers, is devoted to nonclassical thermoelastic modelling of the nonlinear dynamics of shells. Differential equations of different dimensionality and different type have to be combined and nonlinearities of different geometrical, physical or elasto-plastic categories are addressed. Special emphasis is given to the Bubnov--Galerkin method. It can be applied to many problems in the theory of plates and shells, even those with very complex geometries, holes and various boundary conditions. The authors made every effort to keep the text intelligible for both practitioners and graduate students, although they offer a rigorous treatment of both purely mathematical and numerical approaches presented so that the reader can understand, analyse and track the nonlinear dynamics of spatial systems (shells) with thermomechanical behaviours.

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This monograph, addressing researchers as well as engineers, is devoted to nonclassical thermoelastic modelling of the nonlinear dynamics of shells. Differential equations of different dimensionality and different type have to be combined and nonlinearities of different geometrical, physical or elasto-plastic categories are addressed. Special emphasis is given to the Bubnov--Galerkin method. It can be applied to many problems in the theory of plates and shells, even those with very complex geometries, holes and various boundary conditions. The authors made every effort to keep the text intelligible for both practitioners and graduate students, although they offer a rigorous treatment of both purely mathematical and numerical approaches presented so that the reader can understand, analyse and track the nonlinear dynamics of spatial systems (shells) with thermomechanical behaviours.
Content:
Front Matter....Pages I-X
Introduction....Pages 1-13
Coupled Thermoelasticity and Transonic Gas Flow....Pages 15-114
Estimation of the Errors of the Bubnov-Galerkin Method....Pages 115-163
Numerical Investigations of the Errors of the Bubnov-Galerkin Method....Pages 165-178
Coupled Nonlinear Thermoelastic Problems....Pages 179-216
Theory with Physical Nonlinearities and Coupling....Pages 217-227
Nonlinear Problems of Hybrid-Form Equations....Pages 229-347
Dynamics of Thin Elasto-Plastic Shells....Pages 349-390
Unsolved Problems in Nonlinear Dynamics of Shells....Pages 391-403
Back Matter....Pages 405-428

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This monograph, addressing researchers as well as engineers, is devoted to nonclassical thermoelastic modelling of the nonlinear dynamics of shells. Differential equations of different dimensionality and different type have to be combined and nonlinearities of different geometrical, physical or elasto-plastic categories are addressed. Special emphasis is given to the Bubnov--Galerkin method. It can be applied to many problems in the theory of plates and shells, even those with very complex geometries, holes and various boundary conditions. The authors made every effort to keep the text intelligible for both practitioners and graduate students, although they offer a rigorous treatment of both purely mathematical and numerical approaches presented so that the reader can understand, analyse and track the nonlinear dynamics of spatial systems (shells) with thermomechanical behaviours.
Content:
Front Matter....Pages I-X
Introduction....Pages 1-13
Coupled Thermoelasticity and Transonic Gas Flow....Pages 15-114
Estimation of the Errors of the Bubnov-Galerkin Method....Pages 115-163
Numerical Investigations of the Errors of the Bubnov-Galerkin Method....Pages 165-178
Coupled Nonlinear Thermoelastic Problems....Pages 179-216
Theory with Physical Nonlinearities and Coupling....Pages 217-227
Nonlinear Problems of Hybrid-Form Equations....Pages 229-347
Dynamics of Thin Elasto-Plastic Shells....Pages 349-390
Unsolved Problems in Nonlinear Dynamics of Shells....Pages 391-403
Back Matter....Pages 405-428
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