Planes and axes of symmetry in an elastic material
نویسندگان
چکیده
Simple proofs are obtained for the Cowin-Mehrabadi theorem for the identification of a plane of symmetry or an axis of symmetry in an elastic material. The treatment is generalized to a cartesian tensor of arbitrary rank. Necessary and sufficient conditions are found for the existence of a plane of symmetry or an axis of symmetry for a piezoelectric material. Conditions are obtained for the identification of an n -fold axis of symmetry with 3 n .
منابع مشابه
Constitutive Model for Multi-laminate Induced Anisotropic Double Hardening Elastic-plasticity of Sand
A constitutive multi-laminate based elastic-plastic model developed to be capable of accounting induced anisotropic behavior of granular material such as sand. The fabric feature or grain orientation characteristic effects through medium are considered in a rational way under any complex stress path, including cyclic loading. The salient feature of the developed model is a non-associative on pl...
متن کاملA Multi Plane Model for Natural Anisotropy of Sand
Anisotropy of sand is mainly due to the geometrical arrangement of particles that depends on the orientation of applied load respect to the bedding plane. It is geologically due to micro-fabric created by the arrangement of the particles configured during deposition. Most of the models develop using stress/strain invariants are not capable of identifying this kind of anisotropy. This is mainly ...
متن کاملOptimization of Conformal Mapping Functions used in Developing Closed-Form Solutions for Underground Structures with Conventional cross Sections
Elastic solutions applicable to single underground openings usually suffer from geometry related simplification. Most tunnel shapes possess two axes of symmetry while a wide range of geometries used in tunneling practice involve only one symmetry axis. D-shape or horse-shoe shape tunnels and others with arched roof and floor are examples of the later category (one symmetry axis). In the present...
متن کاملA zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope
A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope Abstract A derivation of the Cesàro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the co...
متن کاملA Sub Loading Surface Multilaminate Model for Elastic-Plastic Porous Media
A framework for development of constitutive models based on semi-micromechanical aspects of plasticity is proposed. The resulting of this model for material employed friction type failure criterion, sub-loading surface, and associated flow rule. This model is capable of predicting effects of the rotation of principal stress/strain axes and consequent plastic flow, induced anisotropy of strength...
متن کامل