In this study compressive strength of carbon nanotube (CNT)/cement composite is computed by analytical method. For this purpose representative elementary volume (REV) as an indicator element of composite is chosen and analyzed by elasticity relationships and Von mises' criterion applied to it. It is assumed that carbon nanotubes are distributed uniformly in the cement and there is perfect bonding in the interface of cement and nanotube. At first for simplicity of computations, carbon nanotubes ( CNTs) are assumed to have unidirectional orientation in the cement matrix. In following, the relations are generalized to consider random distribution of nanotubes in cement, and a new factor suggested for random orientation of fibers in the CNT/cement composite. The results of analytical method are compared with experimental results.

In this paper using the eigenvalues and eigenvectors symmetric block diagonal matrices with infinite dimension and numerical method of finite difference a closed form solution for exact solving of Laplace equation is presented. Moreover, the method of this paper has applications in different states of boundary conditions like Newman, Dirichlet and other mixed boundary conditions. Moreover, with the method of this paper, a mathematical model for the exact solution of the Poisson equation is derived. Since these equations have many applications in engineering problems, in each part examples like water seepage problem through the soil and torsion of prismatic bars are presented. Finally the method is provided for torsion problem of prismatic bars with non-circular and non-rectangular cross sections by using of conformal mapping.