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Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
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TL;DR: In this article, the results of linear elastic finite element analyses of stress concentration factors (SCFs) of 80 weld toe T-butt plate geometries are presented in parametric form for tension and pure bending loading.
61 citations
TL;DR: In this article, a one-dimensional exact analytical solution of Biot's equations for the completely general solution of the transient problem in saturated, linear, elastic, porous media is presented.
Abstract: The motions of fluid and solid phases in saturated porous media are coupled by inertial, viscous and mechanical interactions as described by Biot's equations. A one-dimensional exact analytical solution of the Biot's equations for the completely general solution of the transient problem in saturated, linear, elastic, porous media is presented. The problem is solved by using the Fourier series. The transient response of porous media is shown for typical material properties of a natural granular deposit and for different degrees of viscous coupling. The analytical results show the mechanics of dispersive wave propagation in saturated porous media and they should provide a useful comparison term for the existing numerical solution methods.
61 citations
Book•
17 Mar 2005
TL;DR: In this article, the potential theory in 3D linear elasticity has been investigated in the context of bounded-element methods, including the use of hypermersingular and singular residuals as local error estimators.
Abstract: INTRODUCTION TO BOUNDARY METHODS I SELECTED TOPICS IN BOUNDARY ELEMENT METHODS BOUNDARY INTEGRAL EQUATIONS Potential Theory in Three Dimensions Linear Elasticity in Three Dimensions Nearly Singular Integrals in Linear Elasticity Finite Parts of Hypersingular Equations ERROR ESTIMATION Linear Operators Iterated HBIE and Error Estimation Element-Based Error Indicators Numerical Examples THIN FEATURES Exterior BIE for Potential Theory: MEMS BIE for Elasticity: Cracks and Thin Shells II THE BOUNDARY CONTOUR METHOD LINEAR ELASTICITY Surface and Boundary Contour Equations Hypersingular Boundary Integral Equations Internal Displacements and Stresses Numerical Results SHAPE SENSITIVITY ANALYSIS Sensitivities of Boundary Variables Sensitivities of Surface Stresses Sensitivities of Variables at Internal Points Numerical Results: Hollow Sphere Numerical Results: Block with a Hole SHAPE OPTIMIZATION Shape Optimization Problems Numerical Results ERROR ESTIMATION AND ADAPTIVITY Hypersingular Residuals as Local Error Estimators Adaptive Meshing Strategy Numerical Results III THE BOUNDARY NODE METHOD SURFACE APPROXIMANTS Moving Least Squares (MLS) Approximants Surface Derivatives Weight Functions Use of Cartesian Coordinates POTENTIAL THEORY AND ELASTICITY Potential Theory in Three Dimensions Linear Elasticity in Three Dimensions ADAPTIVITY FOR 3-D POTENTIAL THEORY Hypersingular and Singular Residuals Error Estimation and Adaptive Strategy Progressively Adaptive Solutions: Cube Problem One-Step Adaptive Cell Refinement ADAPTIVITY FOR 3-D LINEAR ELASTICITY Hypersingular and Singular Residuals Error Estimation and Adaptive Strategy Progressively Adaptive Solutions: Pulling a Rod One-Step Adaptive Cell Refinement Bibliography Index
61 citations
TL;DR: The mobilizable strength design (MSD) method as discussed by the authors is based on a new application of the theory of plasticity accompanied by the introduction of the concept of "mobilizable soil strength" which can satisfy both safety and serviceability and lead to simple design calculations within which all geotechnical design objectives can be achieved in a single step of calculation.
Abstract: Geotechnical design engineers used to rely on arbitrary rules and definitions of "factor of safety" on peak soil strength in limit analysis calculations. They used elastic stiffness for deformation calculations, but the selection of equivalent linear elastic models was always arbitrary. Therefore, there is a need for a simple unified design method that addresses the real nature of serviceability and collapse limits in soils, which always show a nonlinear and sometimes brittle response. An approach to this method can be based on a new application of the theory of plasticity accompanied by the introduction of the concept of "mobilizable soil strength." This approach can satisfy both safety and serviceabil- ity and lead to simple design calculations within which all geotechnical design objectives can be achieved in a single step of calculation. The proposed method treats a stress path in an element, representative of some soil zone, as a curve of plastic soil strength mobilized as strains develop. Designers enter these strains into a plastic deformation mechanism to predict boundary displacements. The particular case of a cantilevered retaining wall supporting an exca- vation in clay is selected for a spectrum of soil conditions and wall flexibilities. The possible use of the mobilizable strength design (MSD) method in decision-making and design is explored and illustrated.
60 citations
TL;DR: In this paper, the Dirichlet-Eshelby tensor is used to characterize the elastic fields due to inclusions embedded in a finite elastic medium, which is the first paper in a series concerned with the precise characterization of elastic fields.
Abstract: This is the first paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. A novel solution procedure has been developed to systematically solve a type of Fredholm integral equations based on symmetry, self-similarity, and invariant group arguments. In this paper, we consider a two-dimensional (2D) circular inclusion within a finite, circular representative volume element (RVE). The RVE is considered isotropic, linear elastic and is subjected to a displacement (Dirichlet) boundary condition. Starting from the 2D plane strain Navier equation and by using our new solution technique, we obtain the exact disturbance displacement and strain fields due to a prescribed constant eigenstrain field within the inclusion. The solution is characterized by the so-called Dirichlet-Eshelby tensor, which is provided in closed form for both the exterior and interior region of the inclusion. Some immediate applications of the Dirichlet-Eshelby tensor are discussed briefly.
60 citations