Topic
Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a semi-analytical axisymmetric finite element model using the 3D linear elastic theory is developed for free vibrations of functionally graded cylindrical shells made up of isotropic properties.
67 citations
TL;DR: In this article, a hybrid crack element (HCE) is introduced which is powerful and convenient not only for directly determining the SIF but also the coefficients of higher order terms in the plane linear elastic crack tip asymptotic field.
Abstract: An improvement to the extended finite element method (XFEM) and generalised finite element method (GFEM) is introduced. It enriches the finite element approximation of the crack tip node as well as its surrounding nodes with not only the first term but also the higher order terms of the linear elastic crack tip asymptotic field using a partition of unity method (PUM). Numerical results show that together with a reduced quadrature rule to the enriched elements, this approach predicts accurate stress intensity factors (SIFs) directly (i.e. without extra post-processing) after constraining the enriched nodes properly. However, it does not predict accurately the coefficients of the higher order terms. For that a hybrid crack element (HCE) is introduced which is powerful and convenient not only for directly determining the SIF but also the coefficients of higher order terms in the plane linear elastic crack tip asymptotic field. Finally, the general expressions for the coefficients of the second to fifth terms of the linear elastic crack tip asymptotic field of three-point bend single edge notched beams (TPBs) with span to depth ratios widely used in testing are extended to very deep cracks with the use of the HCE.
67 citations
TL;DR: In this paper, the stiffness of three elastic bodies separated by a thin elastic film is studied using a method based on asymptotic expansions and energy minimization, and non-local relations are obtained relating the jumps in the displacements and stress vector fields at one to these fields at order zero.
67 citations
TL;DR: In this article, the effect of spatial grading of adherend elastic modulus on the peak stress and stress distribution in the single-lap bonded joint is studied and the results compared with the traditional uniform modulus adherends using linear elastic finite element analysis.
Abstract: The effect of spatial grading of adherend elastic modulus on the peak stress and stress distribution in the single-lap bonded joint is studied. Single-lap joint with various modulus grading profiles were studied and the results compared with the traditional uniform modulus adherends using linear elastic finite element analysis. Braided preform with continuously varying braid angle was fabricated and the variation of the braid angle measured to realistically evaluate the performance of adherend modulus grading in single-lap bonded joint. The peak stress, stress distribution and transverse displacement at the adhesive mid-thickness were used to compare between the different adherend modulusgrading. The maximum shear stress reduced by about 20% and the shear stress was more uniformly distributed in the adhesive for an actual case of adherend modulus grading. It was also noticed that the joint rotation wasminimum for thisactual case of adherend grading.
67 citations
Book•
31 Jan 2003TL;DR: In this article, Lagrangian and Eulerian descriptions of tensors are given and a generalization of Hooke's law in linear elasticity is presented, which is based on the principle of virtual work.
Abstract: Preface. 1: Tensors. 1. First steps with tensors. 2. Operations of tensors. 3. Euclidean vector space. 4. Exterior algebra. 5. Point spaces. Exercises. 2 : Lagrangian and Eulerian Descriptions. 1. Lagrangian description. 2. Eulerian description. Exercises. 3 : Deformations. 1. Homogeneous transformation. 2. Tangential homogeneous transformation. 3. Infinitesimal transformation. Exercises. 4: Kinematics of Continua. 1. Lagrangian kinematics. 2. Eulerian kinematics. 3. Material derivatives of circulation, flux, and volume. Exercises. 5: Fundamental Laws: Principle of Virtual Work. 1. Conservation of mass and continuity equation. 2. Fundamental laws of dynamics. 3. Theorem of kinetic energy. 4. Study of stresses. 5. Principle of virtual work. 6. Thermomechanics and balance equations. Exercises. 6: Linear Elasticity. 1. Elasticity and tests. 2. Generalized Hooke's law in linear elasticity. 3. Equations and principles in elastostatics. 4. Classical problems. Exercises. Summary of Formulae. Bibliography. Glossary of Symbols. Index.
67 citations