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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Doctoral thesis.</description><language>eng</language><subject>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</subject><creationdate>1994</creationdate><rights>APPROVED FOR PUBLIC RELEASE</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,780,885,27566,27567</link.rule.ids><linktorsrc>$$Uhttps://apps.dtic.mil/sti/citations/ADA334929$$EView_record_in_DTIC$$FView_record_in_$$GDTIC$$Hfree_for_read</linktorsrc></links><search><creatorcontrib>Miller, Kristin L</creatorcontrib><creatorcontrib>AIR FORCE RESEARCH LAB BOLLING AFB DC</creatorcontrib><title>End Effects for Plane Deformations of an Elastic Anisotropic Semi-Infinite Strip</title><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.</description><subject>ANISOTROPY</subject><subject>COMPOSITE STRUCTURES</subject><subject>CONSERVATION</subject><subject>DECAY</subject><subject>DEFORMATION</subject><subject>DIFFERENTIAL EQUATIONS</subject><subject>EDGE EFFECTS</subject><subject>EIGENVALUES</subject><subject>ELASTIC PROPERTIES</subject><subject>ENERGY</subject><subject>ENGINEERING</subject><subject>ESTIMATES</subject><subject>EXPONENTIAL FUNCTIONS</subject><subject>HIGH RATE</subject><subject>ISOTROPIC MATERIALS</subject><subject>ISOTROPISM</subject><subject>LAMINATES</subject><subject>Laminates and Composite Materials</subject><subject>LINEARITY</subject><subject>MATERIALS</subject><subject>Mechanics</subject><subject>NUMERICAL ANALYSIS</subject><subject>ORTHOTROPIC MATERIAL</subject><subject>PLANE DEFORMATIONS</subject><subject>PLANE WAVES</subject><subject>SAINT-VENANT'S PRINICIPLE</subject><subject>SEMI-INFINITE STRIP</subject><subject>STRESS DECAY RATE</subject><subject>STRESSES</subject><subject>Theoretical Mathematics</subject><subject>THESES</subject><fulltext>true</fulltext><rsrctype>report</rsrctype><creationdate>1994</creationdate><recordtype>report</recordtype><sourceid>1RU</sourceid><recordid>eNqFjLEKwjAQhrM4iPoGDvcCXYxLx2AjuhXqXkJ7BwfppeTu_TGDu9P3wcf_H90YZYVIhIspUKkw5iQIAzbfknERhUKQBGJOarxAENZitezNJ9y4ewuxsCFMVnk_uwOlrHj58eSuz_h5vLq1jef2IGhzGIL39_7W-z_5C_hAM58</recordid><startdate>199405</startdate><enddate>199405</enddate><creator>Miller, Kristin L</creator><scope>1RU</scope><scope>BHM</scope></search><sort><creationdate>199405</creationdate><title>End Effects for Plane Deformations of an Elastic Anisotropic Semi-Infinite Strip</title><author>Miller, Kristin L</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-dtic_stinet_ADA3349293</frbrgroupid><rsrctype>reports</rsrctype><prefilter>reports</prefilter><language>eng</language><creationdate>1994</creationdate><topic>ANISOTROPY</topic><topic>COMPOSITE STRUCTURES</topic><topic>CONSERVATION</topic><topic>DECAY</topic><topic>DEFORMATION</topic><topic>DIFFERENTIAL EQUATIONS</topic><topic>EDGE EFFECTS</topic><topic>EIGENVALUES</topic><topic>ELASTIC PROPERTIES</topic><topic>ENERGY</topic><topic>ENGINEERING</topic><topic>ESTIMATES</topic><topic>EXPONENTIAL FUNCTIONS</topic><topic>HIGH RATE</topic><topic>ISOTROPIC MATERIALS</topic><topic>ISOTROPISM</topic><topic>LAMINATES</topic><topic>Laminates and Composite Materials</topic><topic>LINEARITY</topic><topic>MATERIALS</topic><topic>Mechanics</topic><topic>NUMERICAL ANALYSIS</topic><topic>ORTHOTROPIC MATERIAL</topic><topic>PLANE DEFORMATIONS</topic><topic>PLANE WAVES</topic><topic>SAINT-VENANT'S PRINICIPLE</topic><topic>SEMI-INFINITE STRIP</topic><topic>STRESS DECAY RATE</topic><topic>STRESSES</topic><topic>Theoretical Mathematics</topic><topic>THESES</topic><toplevel>online_resources</toplevel><creatorcontrib>Miller, Kristin L</creatorcontrib><creatorcontrib>AIR FORCE RESEARCH LAB BOLLING AFB DC</creatorcontrib><collection>DTIC Technical Reports</collection><collection>DTIC STINET</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Miller, Kristin L</au><aucorp>AIR FORCE RESEARCH LAB BOLLING AFB DC</aucorp><format>book</format><genre>unknown</genre><ristype>RPRT</ristype><btitle>End Effects for Plane Deformations of an Elastic Anisotropic Semi-Infinite Strip</btitle><date>1994-05</date><risdate>1994</risdate><abstract>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.</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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