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Approximate Solution of Plane Orthotropic Elasticity Problems5.

AD702875

Publication Date	1970
Personal Author	Schimke, J.; Thomas, K.; Garrison, J.
Page Count	366
Abstract	The purpose of this study is to compare and evaluate a number of approximate methods for the solution of plane orthotropic elasticity problems. The methods under consideration fall into three main categories. The first category is perturbation methods, which are based on the assumption that the behavior of the orthotropic material under a particular loading is not greatly different than the behavior of some nearby isotropic material under the same loading. The second category is the so-called boundary residual methods. In these techniques the assumed families of functions are required to satisfy all the equations of elasticity internally but none of the boundary conditions. The boundary conditions are then satisfied approximately in accordance with the particular boundary residual criterion under consideration. The two criteria that are examined in this report are the integral least squares and boundary Reissner energy methods. The third category of approximate methods is that for which the assumed functions may have to satisfy some, but not all, of the equations of elasticity internally and certain of the boundary conditions. The other equations of elasticity and the other boundary conditions (if any) are then satisfied approximately in accordance with the particular method. (Author)
Keywords	Structural parts Elasticity Differential equations Approximation(Mathematics) Boundary value problems Perturbation theory Least squares method Matrix algebra Numerical analysis Complex variables Strain(Mechanics) Stresses Composite materials
NTIS Subject Category	46E - Structural Mechanics 72 - Mathematical Sciences
Corporate Authors	Bell Aerosystems CO Buffalo N Y
Document Type	Technical Report
Title Note	Final rept. Apr 68-Oct 69.
NTIS Issue Number	197010
Contract Number	F33615-68-C-1560

Approximate Solution of Plane Orthotropic Elasticity Problems5.

Approximate Solution of Plane Orthotropic Elasticity Problems5.
AD702875

Publication Date	1970
Personal Author	Schimke, J.; Thomas, K.; Garrison, J.
Page Count	366
Abstract	The purpose of this study is to compare and evaluate a number of approximate methods for the solution of plane orthotropic elasticity problems. The methods under consideration fall into three main categories. The first category is perturbation methods, which are based on the assumption that the behavior of the orthotropic material under a particular loading is not greatly different than the behavior of some nearby isotropic material under the same loading. The second category is the so-called boundary residual methods. In these techniques the assumed families of functions are required to satisfy all the equations of elasticity internally but none of the boundary conditions. The boundary conditions are then satisfied approximately in accordance with the particular boundary residual criterion under consideration. The two criteria that are examined in this report are the integral least squares and boundary Reissner energy methods. The third category of approximate methods is that for which the assumed functions may have to satisfy some, but not all, of the equations of elasticity internally and certain of the boundary conditions. The other equations of elasticity and the other boundary conditions (if any) are then satisfied approximately in accordance with the particular method. (Author)
Keywords	Structural parts Elasticity Differential equations Approximation(Mathematics) Boundary value problems Perturbation theory Least squares method Matrix algebra Numerical analysis Complex variables Strain(Mechanics) Stresses Composite materials
NTIS Subject Category	46E - Structural Mechanics 72 - Mathematical Sciences
Corporate Authors	Bell Aerosystems CO Buffalo N Y
Document Type	Technical Report
Title Note	Final rept. Apr 68-Oct 69.
NTIS Issue Number	197010
Contract Number	F33615-68-C-1560