Applied Mechanics and Materials Vol. 684

Abstract: A meshless, barycentric interpolation collocation method for numerical approximation of Darcy flows is proposed. The barycentric Lagrange interpolation and its differentiation matrices are basic tool to discretize governing equations, Dirichlet and Neumann boundary conditions. For Darcy flows in irregular domains, embedding the irregular domain into a rectangular, the barycentric interpolation collocation method can be directly applied. The resultant saddle-point systems come from combining the discretized governing equations and boundary conditions, such that we can deal easy with all kinds of boundary condition either regular or irregular domains. Some numerical examples are given to illustrate the accuracy, stability and robust of presented method.

Abstract: This paper presents theory, experiments and numerical approaches suitable for the solution of straight plane beams rested on an elastic (Winkler's) foundation, including nonlinearities. The nonlinear dependence of the reaction force on displacement in the foundation (i.e. the experimental data) can be described via bilateral linear or bilateral linear + cubic or bilateral linear + cubic + quintic approximations, or by unilateral approximation (i.e. by using the Least Squares Method). These applications lead to linear or nonlinear differential 4^th-order equations. For solutions of nonlinear problems of mechanics, the Finite Difference Method (i.e. the Central Difference Method) and boundary conditions are applied. The solution and its evaluation is performed in second part of this article.

Abstract: This paper presents numerical solutions of straight plane beam structures rested on an elastic (Winkler's) foundation. It is a continuation of our previous work (see Part 1 of this article) focused on practical applications and solutions including nonlinearities in the foundation (i.e. bilateral linear, bilateral linear + cubic, bilateral linear + cubic + quintic approximations and unilateral approximation for dependencies of reaction forces on deflection in the foundation). For solutions of nonlinear problems of mechanics (i.e. differential 4^th-order equations), the Finite Difference Method (i.e. the Central Difference Method) is applied in combination with the Newton (Newton–Raphson) Method. Finally, in one example, linear and nonlinear approaches are solved, evaluated and compared. In some cases, there are evident major differences between the linear and nonlinear solutions.

Abstract: In this paper, according on post rolling maneuver and the flow field, we build a CFD analysis method about momentum source model flow field and aerodynamic characteristics. Preliminary analysis of the numerical has be finished to contrast the difference of post rolling maneuver. The changing law of aerodynamic force, aerodynamic torque variation and the focus position have be given.

Abstract: This paper is concerned with a new model reduced method based on optimal large truncated low-dimensional dynamical system, by which the solution of linear partial differential equation (PDE) is able to be approximate with highly accuracy. The method proposed is based on the weighted residue of PDE under consideration, and the weighted residue is used as an alternative optimal control condition (POT-WR) while solving the PDE. A set of bases is constructed to describe a dynamical system required in case. The Lagrangian multiplier is introduced to eliminate the constraints of the Galerkin projection equation, and the penalty function is used to remove the orthogonal constraint. According to the extreme principle, a set of the ordinary differential equations is obtained by taking the variational operation on generalized optimal function. A conjugate gradients algorithm on FORTRAN code is developed to solve these ordinary differential equations with Fourier polynomials as the initial bases for iterations. The heat transfer equation under a potential initial condition is used to verify the method proposed. Good agreement between the simulations and the analytical solutions of example was obtained, indicating that the POT-WR method presented in this paper provides the most effective posterior way of capturing the dominant characteristics of an infinite-dimensional dynamical system with only finitely few bases.

Abstract: A barycentric interpolation Newton-Raphson iterative method for solving nonlinear beam bending problems is presented in this article. The nonlinear governing differential equation of beam bending problem is discretized by barycentric interpolation collocation method to form a system of nonlinear algebraic equations. Newton-Raphson iterative method is applied to solve the system of nonlinear algebraic equations. The Jacobian derivative matrix in Newton-Raphson iterative method is formulated by the Hadamard product of vectors. Some numerical examples are given to demonstrate the validity and accuracy of proposed method.

Abstract: The surface effect can be significant for nanoscale structures, and the surface energy is expected to be prominent in governing the geometric size-dependent deformation and strength mechanisms of single crystals at the nanoscale. In a new numerical method which combines surface energy and three-dimensional finite element analysis, size effects on the stiffness matrix with surface effects was studied numerically. Results show the surface stiffness matrix is more and more important relative to the bulk stiffness matrix with the size of elements decreasing.

Abstract: The stiffness matrix of volume elements in the traditional finite element methods is symmetry and positive definite. Due to the relatively high surface-to-volume ratio, the surface effect can be significant for nanostructures. In a new numerical method which combines surface energy and three-dimensional finite element analysis, the stiffness matrix with surface effects was computed numerically. Results show the stiffness matrix of surface elements is symmetry and non-positive definite.

Abstract: Based on the similarity theory, the horizontal tail scale model is designed and manufactured. Subsonic doublet lattice method is used to calculate unsteady aerodynamics, V-g method is used to solve the flutter determinant. Optimus software is used to optimize the thickness of the skin. The constraint condition is the frequency, MAC value and flexibility, and the objective function is flutter dynamic pressure. Flutter velocity of horizontal tail model optimized decreased 6%,and flutter frequency increased greatly. Horizontal tail scale model was test in wind tunnel. The finite element calculate results was very close with wind tunnel results, which verify the correctness of the finite element model and optimization models.