Variational theory for Chandrasekharaiah thermopiezoelectricity

Via the semi-inverse method of establishing generalized variational principle for physical problems, a classical variational model (non Gurtin-type and not involving convolutions) for Chandrasekharaiah thermopiezoelectricity is established directly from the governing equations. The present theory aims at providing a more complete theoretical basis for the variational-based finite element applications and variational-based meshless method (element-free method).     

Some basic principles for linear coupled dynamic thermopiezoelectricity

According to the basic idea of classical yin-yang complementarity and modern dualcomplementarity, in a simple and unified way some basic principles for linear coupled dynamic thermopiezoelectricity can be established systematically. An important integral relation in terms of convolutions is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem in linear coupled dynamic thermopiezoelectricity, but also to derive systematically the complementary functionals for eleven-field, nine-field, six-field and three-field simplified Gurtin-type variational principles. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly. Project supported by the National Natural Science Foundation of China (Grant No. 19672074) and Research Grand Council of Hong Kong, No.RGC97/98, HKUST 6055/97E.     

The calculation of bending and stability of a thin rectangular plate for variable rigidity

The subject discussed in this paper is the rectangular plate. Its wwo opposite edges are simply supported, while the other two are arbitrary, and the rigidity of the plate is variable along the direction parallel to the simply supported edges. In order to solve the problem, the author adopts the finite plate-strip element method^[1], which is different from the usual finite element method or the finite strip method. The steps of the above method is no longer to establish a rigidity matrix for elements or strips and gather them into a total matrix for solution. Now the relation of transfer between the strain and inner force of every plate-strip is shown. Finally a practical example is given and this method is found to be easier and more effective.     

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅱ)-THERMOPIEZOELECTRICITY AND MAGNETOTHERMOELASTICITY

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｏｒｙｏｆｍｉｃｒｏｐｏｌｏａｒｔｈｅｒｍｏｅｌａｓｔｉｃｉｔｙｐｒｅｓｅｎｔｅｄｂｙＷ .Ｎｏｗａｃｋｉｉｓｒｅｓｔｕｄｉｅｄｉｎｏｕｒｐａｐｅｒ[1].Ｔｈｉｓｐａｐｅｒｉｓａｄｉｒｅｃｔｃｏｎｔｉｎｕａｔｉｏｎｏｆｒｅｆｅｒｅｎｃｅ [1 ] .Ｔｈｅｐｒｏｂｌｅｍｓｏｃｃｕｒｒｉｎｇｉｎｔｈｅｔｈｅｏｒｉｅｓｏｆｔｈｅｒｍｏｐｉｅｚｏｅｌｅｃｔｒｉｃｉｔｙａｎｄｍａｇｎｅｔｏｔｈｅｒｍｏｅｌａｓｔｉｃｉｔｙｆｏｒｍｉｃｒｏｐｏｌａｒｃｏｎｔｉｎｕａａｒｅｓｉｍｉｌａｒｔ…     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅴ)--POLAR THERMOMECHANICAL CONTINUA

The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity . The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle . The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case , respectively . Finally , the results of micropolar thermopiezoelectricity are directly given .     

FEM analysis on mixed-mode fracture of CSM-GRP

A FEM analysis for studying mixed-mode fracture problem of chopped strand mat glass fibre reinforced polyester laminate is presented. The analysis is formulated on the basis of 8-node quadrilateral isoparametric element. The collapsed triangular quarter-point singular elements were used for calculating stress intensity factors K_Ι and K_Ⅱ.The crack propagation process was computed by implementing constraint release technique. Three different approaches to the solution of stress intensity factors K_Ι and K_Ⅱ were compared. The effect of constraint condition imposed upon the displacement of the three collapsed nodes of the crack tip elements on the K_Ι and K_Ⅱ results was evaluated. The mixed-mode critical stress intensity factors K_ΙC and K_ⅡC were estimated for CSM-GRP through the consideration of K_Ι and K_Ⅱ calculated and the measured failure load and critical crack length in the experiment.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅴ)——POLAR THERMOMECHANICAL CONTINUA

The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity. The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle. The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case, respectively. Finally, the results of micropolar thermopiezoelectricity are directly given. Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931-)     

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅱ)-THERMOPIEZOELECTRICITY AND MAGNETOTHERMOELASTICITY

The theories of thermopiezoelectricity and magnetoelasticity for micropolar continua have been systematically developed by W. Nowacki. In this paper, the theories are restudied. The reason why they were restricted to linear cases is analyzed. The more general conservation principle of energy, energy balance equation and Hamilton principle of thermopiezoelectricity and magnetoelasticity for micropolar continua are established. The corresponding complete equations of motion and boundary conditions as well as balance equations of energy rate for local and nonlocal micropolar thermopiezoelectricity and magnetothermoelasticity are naturally derived. By means of two new functionals and total variation the boundary conditions of displacement, microrotation, electric potential and temperature are also given. Foundation item: the National Natural Science Foundation of China (10072024); the International Cooperation Project of the NSFC (10011130235) and the DFG (51520001); the Research Foundation of the Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931-)     

Thermopiezoelectric Equations for Nonthin Ceramic Shells

The paper presents a method for deriving the differential equations of thermopiezoelectricity for nonthin anisotropic ceramic shells of constant thickness. The method is based on expanding the unknown functions into Fourier’Legendre series in thickness coordinate__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 12–22, February 2005.     

Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load

The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008.