We will derive the fundamental generalized displacement solution, using the Radon transform, and present the direct formulation of the time-harmonic boundary element method (BEM) for the two-dimensional general piezoelectric solids.
The subject of this study is mainly about dynamic response of FRP strengthened masonry walls in terms of fundamental frequency, displacement capacity, shear strength, crack patterns and energy absorption.
The direct integral equation requires a displacement fundamental solution.
Mass, displacement, fundamental frequency and critical load are the objective functions or constraints.
The variation in the nodal circle, fundamental frequency and displacement distribution of the stepped plate are calculated by using finite element method (FEM) under different driving frequencies.
To this end, the displacement fundamental solution (or Green's function) corresponding to a point force for the non-homogenous biharmonic equation in two dimensions are derived in this work by employing a conformal mapping technique in conjunction with the Radon transformation.
u lk * and P lk * represent the fundamental kernels for displacements and tractions, respectively (Portela et al. 1992).
The parametric effects of plate aspect ratio, side-to-thickness ratio, lamination angle schemes and degree of orthotropy on in-plane stresses, transverse shearing stresses, displacements, fundamental frequencies and critical buckling loads are shown.
For this purpose, the equilibrium equation has to be weighted by the fundamental solution of displacements, u *, which leads to:,intlimits_{varGamma } {u_{ki}^ P_{i},{text{d}}varGamma } -,intlimits_{varOmega } {u_{ki,j}^ gamma left[ {C_{ijkl} dot{varepsilon }_{kl} - dot{sigma }_{kl} } right]{text{d}}varOmega } +,intlimitss_{varOmega } {u_{ki}^ b_{i},{text{d}}varOmega } = 0 (23).
By using the obtained fundamental solutions, the extended displacement discontinuity boundary element method is developed to calculate the stress, electric displacement and electric current intensity factors at crack tip.
