Complicated problems in nonlinear mechanics pose a challenge - many cannot be solved with existing closed-form methods. You would probably like easier methods for obtaining analytical and numerically exact solutions for finite elements, updated or total Lagrangian formulation, and arc-length methods of nonlinear elastic problem solving. Nonlinear Mechanics, Second Edition gives you what you want - convenient methods of analysis and valuable data for comparison.
This is the only book to offer a comprehensive treatment of structural components with variable thickness and a variable modulus of elasticity. It is also the only one to cover closed-form solutions for the dynamic and inelastic analysis of members and plates that are subjected to small and large deformations by including axial and vertical restraints. The author uses exact and approximate solutions for static, dynamic, and inelastic analysis. It also discusses aspects of nonlinear vibration of elastically supported beams, nonlinear response of nonuniform rotor blades, and a new concept of airfoil design.
With more than 30% updated and new material, this edition is revised and reorganized to meet the needs of both academia and industry. Easy-to-follow equation derivations, example problems, step-by-step procedures, and iterative approaches create a thorough reference that fills present needs and equips you for the challenges of the future.
• Equilibrium Equations of Bending for Flexible Members
• The Euler-Bernoulli Law of Linear and Nonlinear Deflections
• Integration of the Euler-Bernoulli Nonlinear Differential Equation
• Research Work Associated with the Static and Dynamic Analysis of Flexible Members
• Linear Theory of Equivalent Systems
• Tapered Flexible Cantilever Beams Subjected to Arbitrary Loading Conditions
• Using Rayleigh's Energy Method to Solve the Equivalent Straight Beam
• Differential Equation of Thin Rectangular Plates
• Navier Solution for Simply Supported Rectangular Thin Plates
• Simply Supported Thin Plate with Linear Thickness and Load Variation in the y Direction
• Dynamic Response of Nonuniform Rotor Blades
• New Airfoil Design Concept with Improved Aerodynamic Characteristics
Preface to the First Edition
Preface to the Second Edition
Author
Chapter 1 : Introduction to Nonlinear Mechanics
Chapter 2 : Statically Determinate and Statically Indeterminate Flexible Bars of Uniform and Variable Thickness
Chapter 3 : Inelastic Analysis of Uniform and Variable Thickness Members Subjected to Small Deformations
Chapter 4 : Inelastic Analysis of Flexible Bars of Uniform and Variable Stiffness with and without Axial Restraints
Chapter 5 : Vibration Theory and Analysis of Flexible Members
Chapter 6 : Elastic and Inelastic Analysis of Uniform and Variable Thickness Plates
Chapter 7 : Hysteretic Models and Analysis of Uniform and Variable Stiffness Members under Cyclic Loading
Chapter 8 : Nonlinear Vibration and Instabilities of Elastically Supported Beams
Chapter 9 : Dynamic Response of Nonuniform Rotor Blades and Development of New Airfoil Design with Improved Aerodynamic Characteristics
Appendix A : Simpson’s One-Third Rule
Appendix B : Simply Supported Thin Rectangular Plate Subjected to a Uniformly Distributed Load on Its Upper Surface
Appendix C : Particular Solution of a Certain Differential Equation
Appendix D : Simply Supported Thin Rectangular Plate with Triangular Loading
References
Index
