Nonlinear modeling and analysis of structures is a complex but important step in the design and optimization of modern structural systems. Bridging the gap between the practicing engineer and the applied mathematician, Linear and Nonlinear Structural Mechanics:
∗ Presents mathematically consistent and systematic derivations of comprehensive structural theories
∗ Details the basic principles of linear and nonlinear structural mechanics
∗ Shows how to perform nonlinear structural analysis
∗ Points out important nonlinear structural dynamic behaviors
∗ Provides ready–to–use governing equations and boundary conditions, ranging from simple linear to complex nonlinear ones, for strings, cables, beams, plates, and shells
Designed to be used as a professional reference for structural engineers as well as a graduate–level textbook, this book provides a unique, unified approach that the reader can readily extend to formulate and analyze different or more complex structures.
1.1 Structural Elements.
1.3 Composite Materials.
1.5 Dynamic Characteristics of Linear Discrete Systems.
1.6 Dynamic Characteristics of Nonlinear Discrete Systems
1.7 Analyses of Linear Continuous Systems.
1.8 Analyses of Nonlinear Continuous Systems.
2.1 Principles of Dynamics.
2.2 Strain–Displacement Relations.
2.3 Transformation of Strains and Stresses.
2.4 Stress–Strain Relations.
2.5 Governing Equations.
3. Strings and Cables.
3.1 Modeling of Taut Strings.
3.2 Reduction of String Model to Two Equations.
3.3 Nonlinear Response of Strings.
3.4 Modeling of Cables.
3.5 Reduction of Cable Model to Two Equations.
3.6 Natural Frequencies and Modes of Cables.
3.7 Discretization of the Cable Equations.
3.8 Single–Mode Response with Direct Approach.
3.9 Single–Mode Response with Discretization Approach.
3.10 Extensional Bars.
4.2 Linear Euler–Bernoulli Beam Theory.
4.3 Linear Shear–Deformable Beam Theories.
4.4 Mathematics for Nonlinear Modeling.
4.5 Nonlinear 2–D Euler–Bernoulli Beam Theory.
4.6 Nonlinear 3–D Euler–Bernoulli Beam Theory.
4.7 Nonlinear 3–D Curved Beam Theory Accounting for Warpings.
5. Dynamics of Beams.
5.1 Parametrically Excited Cantilever Beams.
5.2 Transversely Excited Cantilever Beams.
5.3 Clamped–Clamped Buckled Beams.
6. Surface Analysis.
6.1 Initial Curvatures.
6.2 Inplane Strains and Deformed Curvatures.
6.3 Orthogonal Virtual Rotations.
6.4 Variation of Curvatures.
6.5 Local Displacements and Jaumann Strains.
7.2 Linear Classical Plate Theory.
7.3 Linear Shear–Deformable Plate Theories.
7.4 Nonlinear Classical Plate Theory.
7.5 Nonlinear Modeling of Rectangular Surfaces.
7.6 General Nonlinear Classical Plate Theory.
7.7 Nonlinear Shear–Deformable Plate Theory.
7.8 Nonlinear Layerwise Shear–Deformable Plate Theory.
8. Dynamics of Plates.
8.1 Linear Vibrations of Rectangular Plates.
8.2 Linear Vibrations of Membranes.
8.3 Linear Vibrations of Circular and Annular Plates.
8.4 Nonlinear Vibrations of Circular and Annular Plates.
8.5 Nonlinear Vibrations of Rotating Disks.
8.6 Nonlinear Vibrations of Near–Square Plates.
8.8 Thermally Loaded Plates.
9.2 Linear Classical Shell Theory.
9.3 Linear Shear–Deformable Shell Theories.
9.4 Nonlinear Classical Theory for Double–Curved Shells.
9.5 Nonlinear Shear–Deformable Theories for Circular Cylindrical Shells.
9.6 Nonlinear Layerwise Shear–Deformable Shell Theory.
9.7 Nonlinear Dynamics of Infinitely Long Circular Cylindrical Shells.
9.8 Nonlinear Dynamics of Axisymmetric Motion of Closed Spherical Shells.