Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

Spectrum of the Open Asymmetric Simple Exclusion Process with Arbitrary Boundary Parameters

We study the one-dimensional asymmetric simple exclusion process （ASEP） with generic open boundaries （in- cluding current-counting deformation）, and obtain the exact solutions of this ASEP via the off-diagonal Bethe ansatz method. In particular, numerical results for the small size asymmetric simple exclusion process indicate that the spectrum obtained by the Bethe ansatz equations is complete. Moreover, we present the eigenvalue of the totally asymmetric exclusion process and the corresponding Bethe ansatz equations.

Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary conditions.Artificial springs are used to simulate arbitrary boundary conditions.Sanders’shell theory is employed,and von Kármán nonlinear terms are considered in the theoretical modeling.By using Chebyshev polynomials as admissible functions,motion equations are derived with the Ritz method.Then,a direct iteration method is used to obtain the nonlinear vibration frequencies.The effects of the circumferential wave number,the boundary spring stiffness,and the spinning speed on the nonlinear vibration characteristics of the shells are highlighted.It is found that there exist sensitive intervals for the boundary spring stiffness,which makes the variation of the nonlinear frequency ratio more evident.The decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.

Research on Fractal-Scanning Path for Arbitrary Boundary Layer in Layered Manufacturing

The fractal curve is proposed as a novel scanning path used in Layered Manufacturing. Aiming at a limitation that the fractal curve can only fill a square region, a method is developed to realize the trimming of fractal curve in arbitrary boundary layer by means of judging intersection points between parameterized arbitrary boundary and a FASS (space filling, self avoiding, simple and self similar) fractal curve. Accordingly, the related algorithm concerning with determining intersection points has been investigated according to the recursion feature of the fractal curve, and in the process of the fractal curve traversed, the rule of judging intersection points is ascertained as well, so that the laser scanning beam can “walk” along the fractal curve inside the desired boundary, and arbitrary contour components are fabricated.

A modeling method for vibration analysis of cracked beam with arbitrary boundary condition

This paper establishes a cracked Timoshenko beams model to investigate the vibration behavior based on the ultraspherical polynomials.Timoshenko beam theory is applied to model the free vibration analysis of the cracked beam and the numerical results are obtained by using ultraspherical orthogonal polynomials.The boundary conditions of both ends of the cracked beam are modeled as the elastic spring and the beam is divided into two parts by the crack section,and continuous conditions at the connecting face are modeled by the inverse of the flexibility coefficients of fracture mechanics theory.Ignoring the influence of boundary conditions,displacements admissible functions of cracked Timoshenko beam can be set up as ultraspherical orthogonal polynomials.The accuracy and robustness of the present method are evidenced through comparison with previous literature and the results achieved by the finite element method(FEM).In addition,the effects of flexibility coefficient on the natural frequencies are also investigated by using the proposed method.Numerical examples are given for free vibration analysis of cracked beams with various boundary conditions,which may be provided as reference data for future study.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

THE SOLUTION OF A CRACK EMANATING FROM AN ARBITRARY HOLE BY BOUNDARY COLLOCATION METHOD

In this paper a group of stress functions has been proposed for the calculation of a crack emanating from a hole with different shape (including circular, elliptical, rectangular, or rhombic hole) by boundary collocation method. The calculation results show that they coincide very well with the existing solutions by other methods for a circular or elliptical hole with a crack in an infinite plate. At the smae time, a series of results for different holes in a finite plate has also been obtained in this paper. The proposed functions and calculation procedure can be used for a plate of a crack emanating from an arbitrary hole.