Topic
Stress functions
About: Stress functions is a research topic. Over the lifetime, 937 publications have been published within this topic receiving 22085 citations. The topic is also known as: Airy stress function.
Papers published on a yearly basis
1 / 2
Papers
Book•
1 Jan 2000
TL;DR: The Stress Analysis of Cracks Handbook as mentioned in this paper provides a comprehensive, easy-to-access collection of elastic stress solutions for crack configurations, along with other relevant information, such as displacements, crack opening areas, basic stress functions source references, accuracy of solutions, and more.
Abstract: Nearly double the size of the previous edition, the third edition of this classic reference provides a comprehensive, easy-to-access collection of elastic stress solutions for crack configurations. For each configuration, The Stress Analysis of Cracks Handbook present crack tip stress intensity formulas along with other relevant information, such as displacements, crack opening areas, basic stress functions source references, accuracy of solutions, and more. Throughout, it stresses formulas for application to test configurations. The introductory section details the methods of developing the informatio A series of appendices represents special methods and special applications. Now in a hardbound format, the current Handbook offers a number of new features including: * Ne Stress Solutions * Cracked Configurations * Plates with Pinching Loads * Dislocations and Cracks Solutions * Plastic Zone Instability (Expanding a Potentially Interceding "Elastic" Failure Mechanism) * Estimation Methods for Stress Intensity Formulas * J-Integral Methods * Pure Shear Plasticity Solutions. The authors provide 30 new solution pages, plus modifications of older solutions. Contents Include: * Introductory Information Stress Analysis Results for Common Test Specimen Configurations with Cracks * Cracks Along a Single Line * Parallel Cracks * Cracks and Holes or Notches * Curved, Angled, Branched, or Radiating Cracks * Cracks in Reinforced Plates * Three-Dimensional Cracked Configurations * Crack(s) in a Rod or a Plate by Energy Rate Analysis * Strip Yield Model Solutions * Cracks(s) in a Shell * Appendices.
6,800 citations
TL;DR: In this article, a linear theory of deformation of an elastic solid was formulated, in which the potential energy-density is a function of the strain and its first and second gradients.
1,950 citations
TL;DR: In this paper, the general equations for crack-tip stress fields in anisotropic bodies are derived making use of a complex variable approach and stress intensity factors, which permit concise representation of the conditions for crack extension, are defined and evaluated directly from stress functions.
Abstract: The general equations for crack-tip stress fields in anisotropic bodies are derived making use of a complex variable approach. The stress-intensity-factors, which permit concise representation of the conditions for crack extension, are defined and are evaluated directly from stress functions. Some individual boundary value problem solutions are given in closed form and discussed with reference to their companion solutions for isotropic bodies.
1,317 citations
Book•
3 Dec 2012
TL;DR: In this paper, the authors present an analysis of equilibrium boundary-value problems for a nonlinearly elastic body with respect to the Cauchy stress tensor and the almansi tensor.
Abstract: A selection of contents: 1. Deformation of a Continuous Medium. Material coordinates. Spatial coordinates. Vector bases. Deformation gradients. Cauchy-Green and almansi strain measures. Orthogonal tensors accompanying deformation. Dilatation. The oriented elementary area. Variation of the state of strain. The second derivative of a scalar function of a tensor argument. Kinematic relations. Rigid motions. Frame-indifferent tensors. The objective derivative of a tensor. The Rivlin-Ericksen tensors. Tensors of affine deformation. 2. Stress in A Continuous Medium. Body and surface forces. The Cauchy stress tensor. The equations of motion of a continuous medium. The tensor of stress functions. On polar media. Alternative definitions of the stress tensor. The incremental work. 3. The State Equations. The simple body. The principle of material frame-indifference. Elastic materials. The symmetry group of a material. Orthogonal transformation. Isotropic material. The solid body. An isotropic solid material. An elastic fluid. 4. The Equations of Nonlinear Theory of Elasticity and the Statement of Problems. The specific stored energy of deformation. The state equation of an elastic isotropic material. Variation of the stress state. The equilibrium equations for a varied stress state. The relaxation tensor of an isotropic medium. Equations of motion and equilibrium for an isotropic elastic body. Methods of analysis of equilibrium boundary-value problems for a nonlinearly elastic body. The theorem of Ericksen. The principle of stationary complementary energy. The Hamilton-Ostrogradskii principle. 5. The State Equations for a Nonlinearly Elastic Material. On the choice of a state equation for an isotropic elastic body. Seth's body. Signorini's body. Murnaghan's material. A quasi-linear John material. The energy of dilatation and distortion. Empirical criterion. Convexity of the specific strain energy. 6. Problems of the Nonlinear Theory of a Compressible Elastic Medium. The affine transformation of a reference configuration. The uniaxial stretching of a rod. Simple shear. A quasi-linear material. Lame's problem for a cylinder and sphere. The circular membrane. Bending of a strip into a right cylindrical form. Second order effects. The construction of a solution. The dilatation of body subjected to distortion. Second order effects in: The problem of torsion and stretching of a rod in the plane problem for a quasi-linear material. On the "Physically Nonlinear" theory of elasticity. 7. Incompressible Elastic Material. An elastic material with superposed constraints. Second order effects in an incompressible elastic body. The plane deformation of an incompressible material. The universal deformations of an incompressible material. The exact general solutions. Torsion, stretching and change of diameter of a circular cylinder. Lame's problem for a hollow cylinder. The everted cylinder. Lame's problem for a hollow sphere.
658 citations
TL;DR: In this paper, the authors established the skew-symmetric character of the couple-stress tensor in size-dependent continuum representations of matter by relying on the definition of admissible boundary conditions and some kinematical considerations.
528 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 2 |
| 2023 | 2 |
| 2022 | 8 |
| 2021 | 12 |
| 2020 | 21 |
| 2019 | 15 |