Applied Mechanics and Materials Vol. 709

Abstract: The paper contains a brief introduction to the state of the art in poroelasticity models, in BIE & BEM methods application to solve dynamic problems in Laplace domain. Convolution Quadrature Method is formulated, as well as Runge-Kutta convolution quadrature modification and scheme with a key based on the highly oscillatory quadrature principles. Several approaches to Laplace transform inversion, including based on traditional Euler stepping scheme and Runge-Kutta stepping schemes, are numerically compared. A BIE system of direct approach in Laplace domain is used together with the discretization technique based on the collocation method. The boundary is discretized with the quadrilateral 8-node biquadratic elements. Generalized boundary functions are approximated with the help of the Goldshteyn’s displacement-stress matched model. The time-stepping scheme can rely on the application of convolution theorem as well as integration theorem. By means of the developed software the following 3d poroelastodynamic problem were numerically treated: a Heaviside-shaped longitudinal load acting on the face of a column.

Abstract: This paper is devoted to verification of so-called wavelet-based discrete-continual finite element method (wDCFEM), proposed by authors, for three-dimensional problems of local structural analysis. Formulation of the problem for three-dimensional structure with constant physical and geometrical parameters along so-called its basic direction, solutions obtained by wDCFEM and discrete-continual finite element method (DCFEM) and their comparison are presented. It was confirmed that wDCFEM is rather effective in the most critical, vital, potentially dangerous areas of structure in terms of fracture (areas of the so-called edge effects), where some components of solution are rapidly changing functions and their rate of change in many cases can’t be adequately taken into account by the standard finite element method.

Abstract: This paper is devoted to verification of so-called wavelet-based discrete-continual finite element method (wDCFEM), proposed by authors, for three-dimensional problems of local structural analysis. Formulation of the problem for three-dimensional structure with piecewise constant physical and geometrical parameters along so-called its basic direction, solutions obtained by wDCFEM and discrete-continual finite element method (DCFEM) and their comparison are presented. It was confirmed that wDCFEM is rather effective in the most critical, vital, potentially dangerous areas of structure in terms of fracture (areas of the so-called edge effects), where some components of solution are rapidly changing functions and their rate of change in many cases can’t be adequately taken into account by the standard finite element method.

Abstract: Direct boundary element method formulation for transient dynamic linear piezoelectricity is presented. Integral representations of Laplace transformed dynamic piezoelectric fundamental solutions are used. Laplace domain BEM solutions inverted in real time by the stepping method. Numerical example of transient piezoelectric analysis is presented.

Abstract: To describe poroelastic properties, a dynamic model of Biot’s material is used in the frame of the three-dimensional isotropic linear dynamic poroelasticity with four basic functions – displacements of the elastic skeleton and pore pressures. A direct version of the BIE method is developed. The boundary-element scheme is constructed using: regularized BIE’s, a matched element-by-element approximation, adaptive numerical integration in combination with a singularity-reducing algorithm, etc. The computer simulation is done using the boundary-element methodologies of the stepped method.

Abstract: Deflection and stress of simply functionally graded plates are calculated by the meshless collocation method based on generalized multiquadrics radial basis function. The generalized multiquadric radial basis function has the shape parameter c and exponent which have the important effect in the accuracy of the approximation. The deflection and stress of simply functionally graded plates are calculated using the generalized multiquadrics with optimal shape parameter and exponent which is optimized by the genetic algorithm.

Abstract: Though establishing physical modeling of porous hydraulic mufflers, it could derive the transfer matrix. Porous hydraulic muffler attenuation characteristic curve is obtained by MATLAB programming. Through the analysis of characteristic curve, the result showed that the porous hydraulic muffler can effectively absorb fluid pulsation and it is concluded that the change of the structure parameters affect on the attenuation characteristics. It can provide a reference for related research platform.

Abstract: Fiber orientation angles optimization is carried out for maximum fundamental frequency of clamped laminated composite plates using the genetic algorithm. The meshless method is utilized to calculate the fundamental frequency of clamped laminated composite plates. In the present paper, the maximum fundamental frequency is an objective function; design variables are a set of fiber orientation angles in the layers. The examples of square laminated plates are considered. The results for the optimal fiber orientation angles and the maximum fundamental frequencies of the 2-layer plates are presented.

Abstract: The genetic algorithm is used to minimize the stress of the laminated composite plates by optimizing the fiber orientation angle. The objective function of optimization problem is the minimum stress in center of laminated composite plates under the external load; optimization variables are fiber orientation angle. The results for the optimal fiber orientation angle and the minimum stress of the 2-layer plates and 3-layer plates are presented.

Abstract: Layer thickness optimization is performed to maximize the first-order natural frequency of clamped laminated composite plates using the genetic algorithm and meshless global radial basis function collocation method. The objective function of optimization problem is the maximum first-order natural frequency; optimization variables are layer thickness. The optimal layer thickness and the maximum first-order natural frequency of the 2-layer plates are presented to demonstrate the accuracy of present method.