On the basis of Prze mieniecki finite dynamic elements concept, dynamic shape functions, dynamic stif fness and mass matrices of Timoshenko beam element and arbitrary quadrilateral e lement of plate are respectively calculated.
For orthotropic circular cylindrical shells in fluid, at the common boundary of outer surface of shells and flow field, velocity potentials are used to describe flow field, the relationship between the hydrodynamic pressure and the radial displacement are given by the continuous conditions of motion and displacement The equations of fluid-structure coupled vibration are made.
The corresponding shape functions of the resonance line are calculated.
A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations.
The contours of the cylinders are denoted by shape functions ρi = Fi(?i) in local polar coordinate which are then approximated by cubic B-splines instead of trigonometric series.
In order to satisfy the boundary conditions and the crack continuity conditions, the suitable expressions of stress functions and deflection shape functions were put forward.
The shape functions, which determine the cross sectiond2σ/dEdΩ for the inelastic scattering of neutrons as a function of the energy loss?ω and momentum transfer?q, are calculated for the critical region aboveTc of disordered spin systems.
Also, the backscattering form function and resonance spectra, along with the dispersion curves for selected transversely isotropic solid spheres with distinct degrees of material anisotropy, are calculated and discussed.
Data on the influence of an external electric field on the change in the moments of the form function of the absorption band of the complex VGa-SAs in GaAs are obtained.
Although, a closed-form expression relating the cost to reliability may not be a linear; however, in this research, the objective function will always be linear regardless of the shape of the equivalent continuous closed-form function.
In this new form function, the radial displacementu vanishes as radial coordinatesr approach to zero.
However, it is easily seen that, for linear form function of finite element calculation, the displacement continues everywhere, but not the stress components.