Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Spectral Analysis of the Neumann–Poincaré Operator and Characterization of the Stress Concentration in Anti-Plane Elasticity

Abstract: When holes or hard elastic inclusions are closely located, stress which is the gradient of the solution to the anti-plane elasticity equation can be arbitrarily large as the distance between two inclusions tends to zero. It is important to precisely characterize the blow-up of the gradient of such an equation. In this paper we show that the blow-up of the gradient can be characterized by a singular function defined by the single layer potential of an eigenfunction corresponding to the eigenvalue 1/2 of a Neumann–Poincare type operator defined on the boundaries of the inclusions. By comparing the singular function with the one corresponding to two disks osculating to the inclusions, we quantitatively characterize the blow-up of the gradient in terms of explicit functions. In electrostatics, our results apply to the electric field, which is the gradient of the solution to the conductivity equation, in the case where perfectly conducting or insulating inclusions are closely located.

Derivation of a new stiffness matrix for helically armoured cables considering tension and torsion

Abstract: A new element stiffness matrix is derived for straight cable elements subjected to tension and torsion The cross-section of a cable, which may consist of many different structural components, is treated in the following as a single composite element The derivation is quite general; consequently, the results can be used for a broad category of cable configurations Individual helical armourning wires, for instance, may have unique geometric and material properties In addition, no limit is placed on the number of wire layers Furthermore, compressibility of the central core element can also be considered The equations of equilibrium are first derived to include ‘internal’ geometric non-linearties produced by large deformations (axial elongation and rotatioin) of a straight cable element These equations are then linearized in a consistent manner to give a liner stiffness matrix Linear elasticity is assumed throughout Excellent agreement with experimental results for two different cables validates the correctness of the analysis

Mechanics in Material Space: with Applications to Defect and Fracture Mechanics

Abstract: 1 Mathematical Preliminaries.- 1.1 General Remarks.- 1.2 What is a Conservation Law?.- 1.3 Trivial Conservation Laws.- 1.4 System with a Lagrangian Noether's Method.- 1.5 System without a Lagrangian Neutral-Action Method.- 1.6 Discussion.- 2 Linear Theory of Elasticity.- 2.1 General Remarks.- 2.2 Elements of Linear Elasticity.- 2.3 Conservation Laws of Linear Elastostatics.- 2.4 Alternative Derivations of Conservation Laws.- 3 Properties of the Eshelby Tensor.- 3.1 General Remarks 81.- 3.2 Physical Interpretation of the Components of the Eshelby Tensor.- 3.3 Invariants, Principal Values, Principal Directions and Extremal Values of the Eshelby Tensor.- 4 Linear Elasticity with Defects.- 4.1 General Remarks.- 4.2 Path-Independent Integrals and Energy-Release Rates.- 4.3 Example: Hole-Dislocation Interaction.- 4.4 Path-Independent Integrals of Fracture Mechanics.- 5 Inhomogeneous Elastostatics.- 5.1 General Remarks.- 5.2 Symmetry Transformations.- 5.3 The Homogeneous Case.- 5.4 The Inhomogeneous Case.- 5.5 Relation to Stress-Intensity Factors.- 5.6 Examples.- 6 Elastodynamics.- 6.1 General Remarks.- 6.2 Time t as an Additional Independent Variable.- 6.3 Convolution in Time.- 6.4 Domain-Independent Integrals.- 6.5 Energy-Release Rates.- 6.6 Wave Motion.- 7 Dissipative Systems.- 7.1 General Remarks.- 7.2 Diffusion Equation.- 7.3 Non-Linear Wave Equation.- 7.4 Viscoelasticity.- 8 Coupled Fields.- 8.1 General Remarks.- 8.2 Piezoelectricity.- 8.3 Thermoelasticity.- 8.4 Mechanics of a Porous Medium.- 9 Bars, Shafts and Beams.- 9.1 General Remarks.- 9.2 Elements of Strength-of-Materials.- 9.3 Balance and Conservation Laws for Bars and Shafts.- 9.4 Balance and Conservation Laws for Beams.- 9.5 Energy-Release Rates and Stress-Intensity Factors.- 9.6 Examples.- 10 Plates and Shells.- 10.1 General Remarks.- 10.2 Plate Theories.- 10.3 Conservation Laws for Elastostatics of Mindlin Plates.- 10.4 Reduction to the Classical Theory.- 10.5 Conservation Laws for Shells.- Appendix A.- Conservation Laws for Inhomogeneous Bars under Arbitrary Axial Loading.- Appendix B.- B.1 Elastodynamics of Inhomogeneous Bernoulli-Euler Beams.- B.2 Reduction to Statics.- Appendix C.- C.1 Elastodynamics of Inhomogeneous Mindlin Plates.- C.2 Reduction to Statics.- References.- Symbol Index.- Author Index.

Mathematical Modeling in Continuum Mechanics

Abstract: Part I. Fundamental Concepts in Continuum Mechanics: 1. Describing the motion of a system: geometry and kinematics 2. The fundamental law of dynamics 3. The Cauchy stress-tensor. Applications 4. Real and virtual powers 5. Deformation tensor. Deformation rate tensor. Constitutive laws 6. Energy equations. Shock equations Part II. Physics of Fluids: 7. General properties of Newtonian fluids 8. Flows of perfect fluids 9. Viscous fluids and thermohydraulics 10. Magnetohydrodynamics and inertial confinement of plasmas 11. Combustion 12. Equations of the atmosphere and of the ocean Part III. Solid Mechanics: 13. The general equations of linear elasticity 14. Classical problems of elastostatics 15. Energy theorems. Duality. Variational formulations 16. Introduction to nonlinear constitutive laws and to homogenization Part IV. Introduction to Wave Phenomena: 17. Linear wave equations in mechanics 18. The soliton equation: the Korteweg-de Vries equations 19. The nonlinear Schrodinger equation Appendix A.