Classical methods of two-dimensional elasticity can be extended to give an exact solution of the three-dimensional problem for the beam — i.e. a general solution for the prismatic bar loaded on its lateral surfaces, subject only to the restriction that the tractions can be expanded as power series in the axial coordinate z. A series of sub-problems Pj is defined by successive partial differenti...

This paper presents an analytical solution for response of a piezoelectric hollow cylinder under two-dimensional electro thermo mechanical fields. The solution is based on a direct method and the Navier equations were solved using the complex Fourier series. The advantage of this method is its generality and from mathematical point of view, any type of the thermo mechanical and electrical bound...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...