Thermo-Dynamics of Plates and Shells (eBook)

Preface 5
Table of Contents 8
1 Three–Dimensional Problems of Theory of Plates in Temperature Field 12
1.1 Introduction 13
1.2 Coupled 3D Thermoelasticity Problem for a Cubicoid 22
1.3 Methods of Solving Difference Equations 50
1.4 Linear Problems in the Theory of Plates in 3D Space 70
1.5 3D Physically Non-Linear Problems 140
2 Stability of Rectangular Shells within Temperature Field 160
2.1 Introduction 161
2.2 Flexible Anisotropic Shallow Shells in Temperature Fields 163
2.3 Solution of 3D Stationary Heat Transfer Equation 197
2.4 Algorithm for Difference Equations 238
2.5 Computations of Plates and Shells in a Temperature Field 263
3 Dynamical Behaviour and Stability of Closed Cylindrical Shells with Continuous Thermal Load 278
3.1 Introduction 278
3.2 Thermoelastic Thin Thermosensitive Cylindrical Shells 287
3.3 Computational Algorithms 321
3.4 Dynamical Stability Loss with Ununiform Force Excitation 345
3.5 Dynamical Stability Loss and Non-uniform Thermal Load 377
4 Dynamical Behaviour and Stability of Rectangular Shells with Thermal Load 406
4.1 Introduction 406
4.2 Algorithm 413
4.3 Stability of Thin Shallow Shells 443
4.4 Stability of Thin Conical Shells 469
4.5 Stability of Flexurable Conical Shells with Convection 490
5 Dynamical Behaviour and Stability of Flexurable Sectorial Shells with Thermal Load 504
5.1 Introduction 504
5.2 Flexurable Conical Sectorial Shells Computations 509
5.3 Stability of Sectorial Shells with Finite Deflections 531
5.4 Chaotic Dynamics of Sectorial Shells 625
6 Coupled Problems of Thin Shallow Shells in a Temperature Field within Kirchhoff- Love Kinematic Model 644
6.1 Introduction 644
6.2 Fundamental Assumptions and Relations 645
6.3 Differential Equations 647
6.4 Boundary and Initial Conditions 650
6.5 Solution to 3D heat conductivity equation 651
6.6 Algorithm 653
6.7 Stability Rectangular Shells with Coupled Deformation and temperature fields 656
6.8 Additional Method 677
7 Novel Solution Method for a System of Linear Algebraic Equations 682
7.1 Introduction 682
7.2 Elimination method for equations 684
7.3 Numerical solution of a three-dimensional equation of elliptic type 695
7.4 Computation of geometrically non-linear non-homogenous shallow shells with mixed boundary condition along their sides 707
8 Mathematical Approaches to Coupled Termomechanical Problems 716
8.1 Existence and Uniqueness of Solution of One Coupled Plate Thermomechanics Problem 716
8.2 On the Solution of a Coupled Thermo-mechanical Problem for Non- homogeneous Timoshenko- type Shells 724
8.3 On the Solvable Operators Generated by Uniformly Correct Problems 730
References 734
Index 778