In this study, a layered beam element based on a higher-order theory is presented for bending analysis of laminated composites. This is an N-layer element which contains (9N + 7) degrees-of-freedom. The element stiffness matrix is derived by means of the Lagrange equations. Deflections and stresses in laminated beams with different end conditions and stacking order are calculated numerically. The results are compared with those available in the literature to show the accuracy of element.
The time-dependent Ginzburg-Landau equations have been solved numerically by a finite element analysis for the mesoscopic superconducting samples with cylindrical shape in a uniform axial magnetic field. We obtain the different vortex patterns as a function of the applied field perpendicular to its surface. We find that multi-vortex states are ground state in three-dimensional mesoscopic cylinders. These results show that our approach is an effective and useful to interpret experimental data on vortex states in the mesoscopic superconductors.
The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.