Nguồn ngoài

Structural Mechanics

This text covers the fundamental concepts of structural mechanics with applications to marine, civil, and mechanical structures. Topics include analysis of small deflections of beams, moderately large deflections of beams, columns, cables, and shafts; elastic and plastic buckling of columns, thin walled sections and plates; exact and approximate methods; energy methods; principle of virtual work; introduction to failure analysis of structures.

Mechanical Engineering Engineering

Tác giả: Tomasz Wierzbicki
Nhà xuất bản: Massachusetts Institute of Technology
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN

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Mục lục· 89 mục

01: The Concept of Strain
1.01: One-dimensional Strain
1.02: Extension to the 3-D case
1.03: Description of Strain in the Cylindrical Coordinate System
1.04: Kinematics of the Elementary Beam Theory
1.05: Euler-Bernoulli Hypothesis
1.06: Strain-Displacement Relation of Thin Plates
1.07: Advanced Topic- Derivation of the Strain-Displacement Relation for Thin Plates
1.08: Expanded Form of Strain-Displacement Relation
1.09: Moderately Large Deflections of Beams and Plates
1.10: Strain-Displacement Relations for Circulate Plates
02: The Concept of Stress, Generalized Stresses and Equilibrium
2.01: Stress Tensor
2.02: Advanced Topic - Local Equilibrium from the Principle of Virtual Work
2.03: Generalized Forces and Bending Moments in Plates
2.04: Advanced Topic - Principle of Virtual Work for Beams
2.05: Derivation of Equation of Equilibrium for Beams from the Principle of Virtual Work
2.06: Advanced Topic - Mathematical Theory of Beams
2.07: Equilibrium in the Theory of Moderately Large Deflections of Beams
2.08: Equilibrium of Rectangular Plates
2.09: Circular Plates
03: Development of Constitutive Equations of Continuum, Beams and Plates
3.01: Prologue to Development of Constitutive Equations for Continuum, Beams and Plates
3.02: Elasticity Law in 3-D Continuum
3.03: Specification to the 2-D Continuum
3.04: Hook’s Law in Generalized Quantities for Beams
3.05: Inconsistencies in the Elementary Beam Theory
3.06: Derivation of Constitutive Equations for Plates (Advanced)
3.07: Stress Formula for Plates
04: Solution Method for Beam Deflections
4.01: Governing Equations
4.02: General Properties of the Beam Governing Equation- General and Particular Solutions
4.03: Statically Determined Beams
4.04: Continuity Conditions, an Example
05: Moderately Large Deflection Theory of Beams
5.01: General Formulation
5.02: Solution for a Beam on Roller Support
5.03: Solution for a Beam with Fixed Axial Displacements
5.04: Galerkin Method of Solving Non-linear Differential Equation
5.05: Generalization to Arbitrary Non-linear Problems in Plates and Shells
06: Bending Response of Plates and Optimum Design
6.01: Beam Deflection Equation
6.02: Deflections of Circular Plates
6.03: Equivalence of Square and Circular Plates
6.04: Design Concept for Plates
6.05: Sandwich Plates
6.06: Stiffened Plates
6.07: Plates versus Grillages
6.08: The Concept of Equivalent Thickness
6.09: Shear Lag
07: Energy Methods in Elasticity
7.01: The Concept of Potential Energy
7.02: Equivalence of the Minimum Potential Energy and Principle of Virtual Work
7.03: Two Formulations for Beams
7.04: Fourier Series Expansion and the Ritz Method
7.05: Solution by Taylor expansion
7.06: Castigliano Theorem
08: Stability of Elastic Structures
8.01: Prelude to Stability of Elastic Structures
8.02: Trefftz Condition for Stability
8.03: Stability of Elastic Column Using the Energy Method
8.04: Effect of Structural Imperfections
8.05: Stability in Tension
8.06: Plastic Buckling of Columns
8.07: Mode Transition (Advanced)
09: Advanced Topic in Column Buckling
9.01: The Tallest Column
9.02: Deflection Behavior for Beam with Compressive Axial Loads and Transverse Loads
9.03: Snap-through of a Two Bar System
9.04: Dynamic Snap-Through
10: Buckling of Plates and Sections
10.01: Governing Equations and Boundary Conditions
10.02: Buckling of a Simply Supported Plate
10.03: Effect of Boundary Conditions
10.04: Buckling of Sections
10.05: Post-buckling Response of Plates (Advanced)
10.06: Ultimate Strength of Plates
10.07: Effect of Initial Imperfection
11: Fundamental Concepts in Structural Plasticity
11.01: Hardening Curve and Yield Curve
Unloading Condition
11.03: Incompressibility
11.04: Yield Condition
11.05: Isotropic and Kinematic Hardening
11.06: Flow Rule
11.07: Derivation of the Yield Condition from First Principles (Advanced)
11.08: Tresca Yield Condition
11.09: Experimental Validation
11.10: Example of the Design against First Yield