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THE BASIC SOLUTION OF A 3-D RECTANGULAR PERMEABLE CRACK IN A PIEZOELECTRIC/PIEZOMAGNETIC COMPOSITE MATERIAL

Acta Mechanica Solida Sinica 2013年第4期26卷 403-418页

作者： Yuling Tang Zhengong Zhou Linzhi Wu Center for Composite Materials and Structures Harbin Institute of Technology

The solution of a 3-D rectangular permeable crack in a piezoelectric/piezomagnetic composite material was investigated by using the generalized Almansi＇s theorem and the Schmidt *** problem was formulated through Fourier transform into three pairs of dual integral equations,in which the unknown variables are the displacement jumps across the crack *** solve the dual integral equations,the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi ***,the relations between the electric filed,the magnetic flux field and the stress field near the crack edges were obtained and the effects of the shape of the rectangular crack on the stress,the electric displacement and magnetic flux intensity factors in a piezoelectric/piezomagnetic composite material were analyzed.

关键词： piezoelectric/piezomagnetic media rectangular crack mechanics of solids

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MULTIPLE PARALLEL SYMMETRIC PERMEABLE MODEL-Ⅲ CRACKS IN A PIEZOELECTRIC/PIEZOMAGNETIC COMPOSITE MATERIAL PLANE

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Acta Mechanica Solida Sinica 2010年第4期23卷 336-352页

作者： Zhengong Zhou Peiwei Zhang Linzhi Wu P.O.Box 3010 No.2 Yikuang Street Center for Composite Materials and Structures Harbin Institute of Technology Harbin 150080 China

In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt *** problem is formulated through Fourier transform into dual integral equations, in which the unknown variables are the displacement jumps across the crack *** solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi ***, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is *** results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the *** is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials.

关键词： piezoelectric/piezomagnetic composites multiple parallel symmetric cracks crack shielding effect mechanics of solids

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On Applications of Generalized Functions in the Discontinuous Beam Bending Differential Equations

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Applied Mathematics 2016年第16期7卷 1943-1970页

作者： Dimplekumar Chalishajar Austin States Brad Lipscomb Department of Applied Mathematics Virginia Military Institute (VMI) Lexington USA

This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta function. The governing differential Equation is Euler-Bernoulli beams with jump discontinuities on displacements and rotations. Also, the governing differential Equations of a Timoshenko beam with jump discontinuities in slope, deflection, flexural stiffness, and shear stiffness are obtained in the space of generalized functions. The operator of one of the governing differential Equations changes so that for both Equations the Dirac Delta function and its first distributional derivative appear in the new force terms as we present the same in a Euler-Bernoulli beam. Examples are provided to illustrate the abstract theory. This research is useful to Mechanical Engineering, Ocean Engineering, Civil Engineering, and Aerospace Engineering.

关键词： mechanics of solids Discontinuities in a Beam Bending Differential Equations Generalized Functions Jump Discontinuities

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