Using the Frobenius series method (FSM), an analytical solution is developed to obtain mechanical stresses of thick spherical pressure vessels made of functionally graded materials (FGMs). The cylinder pressure vessel is subjected to uniform internal pressure. The modulus of elasticity is graded along the radial direction according to power functions of the radial direction. It is assumed that ...

One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the ε-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to sta...

Although wood is used as a favourite building material among concrete and steel, the mechanical behaviour was not scientifically investigated yet as one would expect. To be able to perform more realistic simulations of timber structures by means of modern numerical simulation methods like the Finite Element Method (FEM), a suitable constitutive material model is required. Such a material model ...

We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed usingGreen-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the di...

We compare numerically the performance of a new continuous-discontinuous finite element method (CDFEM) for linear convection-diffusion equations with three well-known upwind finite element formulations, namely with the streamline upwind Petrov-Galerkin finite element method, the residualfree bubble method and the discontinuous Galerkin finite element method. The defining feature of the CDFEM is...

The finite element method (FEM) has been commonly employed in a variety of fields as a computer simulation method to solve such problems as solid, fluid, electro-magnetic phenomena and so on. However, creation of a quality mesh for the problem domain is a prerequisite when using FEM, which becomes a major part of the cost of a simulation. It is natural that the concept of meshless method has ev...

In electronic devices solder joints form a mechanical as well as an electrical connection between the circuit board and the component (e.g. a chip or a resistor). Temperature variations occurring during field use cause crack initiation and crack growth inside the joints. Accurate prediction of the lifetime requires a method to simulate the damage process based on microstructural properties. Num...

Isogeometric analysis, as a special field of the finite element method (FEM) which integrates geometric and finite element mesh modelling, is one of the promising directions of FEM development. The paper presents a concept of isogeometric FEM analysis of thin-walled structures based on the Kirchhoff-Love shell formulation and NURBS as basis functions. The basic properties of isogeometric shell ...