We present expressions for the Green's tensors in terms of lattice sums for general two-dimensional arrays in both elastostatics and elastodynamics. We represent the lattice sums in rapidly{convergent forms by Fourier transform methods. We compare the static lattice sums with recently published, highly accurate values for square arrays. We also establish Rayleigh identities for elastostatic and...

We present algorithms for the crackand inclusion problem in planar linear elastostatics. The algorithms are based on new integral equations. For the pure crack problem the integral equations are of Fredholm’s second kind. Our algorithms show great stability and allow for solutions to problems more complex than previously has been possible. Our results are orders of magnitudes more accurate than...

In this paper, we introduce and study a new unified and general class of variational inequalities. We derive the general error estimates for the finite element solutions of variational inequalities. It has been shown that a class of contact problems with friction terms arising in elastostatics can be studied in the framework of variational inequalities. Several special cases, which can be obtai...