End Effects for Plane Deformations of an Elastic Anisotropic Semi-Infinite Strip

In the linear theory of elasticity, Saint-Venant's principle is used to justify the neglect of edge effects when determining stresses in a body. For isotropic materials, the validity of this is well established. However for anisotropic materials, experimental results have shown that edge effect...

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description In the linear theory of elasticity, Saint-Venant's principle is used to justify the neglect of edge effects when determining stresses in a body. For isotropic materials, the validity of this is well established. However for anisotropic materials, experimental results have shown that edge effects may persist much farther into the material than for isotropic materials and as a result cannot be neglected. This research examines the effect of material anisotropy on the exponential decay rate for stresses in a semi-infinite elastic strip. A linear elastic semi-infinite strip in a state of plane stress/strain subject to a self-equilibrated end load is considered first for a specially orthotropic material and then for the general anisotropic material. The problem is governed by a fourth-order elliptic partial differential equation with constant coefficients. Conservation properties of the solution are derived to help to determine a stress decay rate estimate. Energy methods are then used to establish lower bounds on the actual stress decay rate. Both analytic and numerical estimates are obtained in terms of the elastic constants of the material and results are shown for several contemporary engineering materials. When compared with the exact stress decay rate computed numerically from the eigenvalues of a fourth-order ordinary differential equation, the results in some cases show a high degree of accuracy. Results of the type obtained here have several important practical applications. Doctoral thesis.
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For isotropic materials, the validity of this is well established. However for anisotropic materials, experimental results have shown that edge effects may persist much farther into the material than for isotropic materials and as a result cannot be neglected. This research examines the effect of material anisotropy on the exponential decay rate for stresses in a semi-infinite elastic strip. A linear elastic semi-infinite strip in a state of plane stress/strain subject to a self-equilibrated end load is considered first for a specially orthotropic material and then for the general anisotropic material. The problem is governed by a fourth-order elliptic partial differential equation with constant coefficients. Conservation properties of the solution are derived to help to determine a stress decay rate estimate. Energy methods are then used to establish lower bounds on the actual stress decay rate. Both analytic and numerical estimates are obtained in terms of the elastic constants of the material and results are shown for several contemporary engineering materials. When compared with the exact stress decay rate computed numerically from the eigenvalues of a fourth-order ordinary differential equation, the results in some cases show a high degree of accuracy. Results of the type obtained here have several important practical applications. 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For isotropic materials, the validity of this is well established. However for anisotropic materials, experimental results have shown that edge effects may persist much farther into the material than for isotropic materials and as a result cannot be neglected. This research examines the effect of material anisotropy on the exponential decay rate for stresses in a semi-infinite elastic strip. A linear elastic semi-infinite strip in a state of plane stress/strain subject to a self-equilibrated end load is considered first for a specially orthotropic material and then for the general anisotropic material. The problem is governed by a fourth-order elliptic partial differential equation with constant coefficients. Conservation properties of the solution are derived to help to determine a stress decay rate estimate. Energy methods are then used to establish lower bounds on the actual stress decay rate. Both analytic and numerical estimates are obtained in terms of the elastic constants of the material and results are shown for several contemporary engineering materials. When compared with the exact stress decay rate computed numerically from the eigenvalues of a fourth-order ordinary differential equation, the results in some cases show a high degree of accuracy. Results of the type obtained here have several important practical applications. 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Both analytic and numerical estimates are obtained in terms of the elastic constants of the material and results are shown for several contemporary engineering materials. When compared with the exact stress decay rate computed numerically from the eigenvalues of a fourth-order ordinary differential equation, the results in some cases show a high degree of accuracy. Results of the type obtained here have several important practical applications. Doctoral thesis.</abstract><oa>free_for_read</oa></addata></record>
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subjects ANISOTROPY
COMPOSITE STRUCTURES
CONSERVATION
DECAY
DEFORMATION
DIFFERENTIAL EQUATIONS
EDGE EFFECTS
EIGENVALUES
ELASTIC PROPERTIES
ENERGY
ENGINEERING
ESTIMATES
EXPONENTIAL FUNCTIONS
HIGH RATE
ISOTROPIC MATERIALS
ISOTROPISM
LAMINATES
Laminates and Composite Materials
LINEARITY
MATERIALS
Mechanics
NUMERICAL ANALYSIS
ORTHOTROPIC MATERIAL
PLANE DEFORMATIONS
PLANE WAVES
SAINT-VENANT'S PRINICIPLE
SEMI-INFINITE STRIP
STRESS DECAY RATE
STRESSES
Theoretical Mathematics
THESES
title End Effects for Plane Deformations of an Elastic Anisotropic Semi-Infinite Strip
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