Hwu, C. September 1, September ; 57 3 : — In the case when an anisotropic plate contains a triangular, oval, or square opening, the only solution available in the literature is an approximate solution for orthotropic plates with openings, which was obtained by Lekhnitskii using the complex variable formulation. Solutions for any kind of anisotropic plates with various openings are presented in this paper by applying the Stroh formalism and using the technique of conformal mapping. Unlike the former results, which have different orders of approximation for different openings, the solutions presented here have only one simple unified expression for various openings such as the ellipse, circle, crack, triangle, oval, and square.
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Louis, Missouri and T. All rights reserved. Serget Georgievich Anisotropic plates. Translation of: Anizotropnye plastinki.. Includes indexes. Plates Engineering I. P6LA State of stress in a continuous body 2. Curvilinear anisotropy 4. State of generalized plane stress of a homogeneous plate. General expressions for stress functions. Relation between plane problems and functions of complex variables.
Determination of elastic constants for a new coordinate system. Change of complex parameters due to coordinate transfor- mation 11, Elastic constants for certain anisotropic plates The simplest cases 14, Bending of a beam by an end force 15, Bending of a beam by a uniformly distributed load Bending of a beam by a linearly distributed load Bending of a beam by an arbitrary load Deformation of a wedge-shaped body by a force applied at the apex Bending of a wedge-shaped body by moments 22, Bending of a wedge-shaped body by a distributed load Pure bending of a curved beam with cylindrical anisotropy Bending of a curvilinear anisotropic curved beam by an end force Bending of a curved curvilinear anisotropic curved beam by a distributed load Stress distribution in an annular plate with cylindrical aniso- tropy Stress distribution in a composite curvilinear anisotropic ring Effect of a concentrated force and moment applied at the edge Effect of a force and moment applied to a point in an clastic plate Stress distribution in an elliptic plate loaded along the edge Stress distribution in a rotating homogeneous elliptic plate Stress distribution in a rotating curvilinear anisotropic disc Stress determination in a plate with an elliptic opening Special cases of loading Stress distribution in an orthotropic plate with a circular opening Stress distribution in an orthotropic plate with a circular open- ing cont.
Stress distribution in a plate with an elliptic core Special cases of a plate with an elliptic core Plate with a circular core subjected to tangential force Plane problem for a slightly anisotropic plate Stress determination in a slightly anisotropic plate with an opening Tension and pure bending of a slightly anisotropic plate with a square opening Formulas for a plate with an opening of special shape Stress determination in a plate with triangular opening Tension of an orthotropic plate with a triangular opening Pure bending of an orthotropic plate with a triangular opening Stress determination in plate with an oval opening Tension of an orthotropic plate with an oval opening Pure bending of an orthotropic plate with an oval opening Tension of an orthotropic plate with a square opening Approximate theory of bending of anisotropic plates thin plates 22 Equations of deflected surface and boundary conditions Relation between the theory of bending with the theory of func- tions of a complex variables 64, Equation of a deflected surface with consideration of membrane forces.
Plates with large deflections on an elastic foundation Determination of rigidities and reduced moduli of multi-layered plates Rigidities and reduced moduli of plates consisting of identical layers Determination of the plate rigidities with moduli which change with the plate thickness Calculation of rigidities for arbitrary directions The simplest cases of bending Bending of an orthotropic rectangular plate with clamped edges Bending of an orthotropic rectangular plate with two edges clamped Bending of an orthotropic rectangular plate by a uniformly distributed load Bending of a strip with clamped sides Application of the theory of bending of an orthotropic strip Bending of a rectangular orthotropic strip strengthened by parallel rigid ribs Influence functions for an orthotropic plate with supported sides Bending of a plate with one rib Bending of a homogeneous elliptic and circular plate clamped along the edge Bending of a circular curvilinear anisotropic plate by symmetric loading Bending of a circular curvilinear anisotropic plate by a concen- trated force Approximate methods for the determination of deflections of anisotropic plates Approximate solutions for rectangular plates Local stresses near the rectangular edge of a plate.
Effect of a concentrated moment Bending of a plate with an elliptic opening, the edge of which is loaded arbitrarily Pure bending of a plate weakened by a circular opening Free vibrations of plates Frequency determination ofa rectangular orthotropic plate Approximate methods for frequency determination Examples of the frequency determination in the first approxi- mation General problem of the stability of plates Basic methods for the determination of a critical load
Anisotropic Elastic Plates
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Anisotropic Elastic Plates find wide applications as structural elements in modern technology. The plates are considered to be subjected to not only inplane loads but also transverse loads. Plane problems, plate bending problems as well as stretching-bending coupling problems are all treated in this book. In addition to the introduction of the theory of anisotropic elasticity that includes two complex variable methods - Lekhnitiskii formalism and Stroh formalism- several important subjects are also discussed such as wedges, interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermal stresses and boundary element analysis. Anisotropic Elastic Plates also collects over one hundred problems and solutions. This book is a useful resource for engineers and researchers in composite materials. Skip to main content Skip to table of contents.