Elastodynamics and Elastostatics by a Unified Method of Potentials for x3-Convex Domains

被引：0

作者：

Morteza Eskandari-Ghadi

Ronald Y. S. Pak

机构：

[1] University of Tehran,Department of Engineering Science, Faculty of Engineering

[2] University of Colorado,Department of Civil, Environmental and Architectural Engineering

来源：

Journal of Elasticity | 2008年 / 92卷

关键词：

Dynamics; Statics; Elasticity; Displacement potentials; Completeness; Wave propagation; Solid mechanics; 74B05; 74J05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A new general solution in terms of two scalar potential functions for classical elastodynamics of x3-convex domains is presented. Through the establishment and usage of a set of basic mathematical lemmas, a demonstration of its connection to Kovalevshi–Iacovache–Somigliana elastodynamic solution, and thus its completeness, is realized with the aid of the theory of repeated wave equations and Boggio’s theorem. With the time dependence of the potentials suppressed, the new decomposition can, unlike Lamé’s, degenerate to a complete solution for elastostatic problems.

引用

页码：187 / 194

页数：7

共 13 条

[1]

Eskandari-Ghadi M.(2005)A complete solution of the wave equations for transversely isotropic media J. Elast. 81 1-19

[2]

Gurtin M.E.(1962)On Helmholtz’s theorem and the completeness of the Papkovich-Neuber stress functions for infinite domains Arch. Ration. Mech. Anal. 9 225-233

[3]

Pak R.Y.S.(1987)Asymmetric wave propagation in an elastic half-space by a method of potentials J. Appl. Mech., ASME 54 121-126

[4]

Pak R.Y.S.(2007)On the completeness of a method of potentials in elastodynamics Quart. Appl. Math. 65 789-797

[5]

Eskandari-Ghadi M.(2002)Three-dimensional Green’s functions for a multi-layered half-space by displacement potentials J. Engrg. Mech., ASCE 128 449-461

[6]

Pak R.Y.S.(1960)On the integration of the equation of motion in the classical theory of elasticity Arch. Ration. Mech. Anal. 6 34-50

[7]

Guzina B.B.(1957)On stress functions for elastokinetics and the integration of the repeated wave equation Quart. Appl. Math. 15 149-153

[8]

Sternberg E.(1969)Completeness of Papkovich potentials Quart. Appl. Math. 26 477-483

[9]

Sternberg E.(1995)On the completeness and uniqueness of Papkovich-Neuber and the non-axissymetric Boussinesq, Love and Burgatti solutions in general cylindrical coordinates J. Elast. 36 227-255

[10]

Eubanks R.A.(1959)Invariant and complete stress functions for general continua Arch. Ration. Mech. Analy. 4 1-29

← 1 2 →