Search results

The problems of shear flexible beams are analyzed by the MLPG method based on a locking‐free weak formulation. In order for the weak formulation to be locking‐free, the numerical characteristics of the variational functional for a shear flexible beam, in the thin beam limit, are discussed. Based on these discussions a locking‐free local symmetric weak form is derived by changing the set of two dependent variables in governing equations from that of transverse displacement and total rotation to the set of transverse displacement and transverse shear strain. For the interpolation of the chosen set of dependent variables (i.e. transverse displacement and transverse shear strain) in the locking‐free local symmetric weak form, the recently proposed generalized moving least squares (GMLS) interpolation scheme is utilized, in order to introduce the derivative of the transverse displacement as an additional nodal degree of freedom, independent of the nodal transverse displacement. Through numerical examples, convergence tests are performed. To identify the locking‐free nature of the proposed method, problems of shear flexible beams in the thick beam limit and in the thin beam limit are analyzed, and the numerical results are compared with analytical solutions. The potential of using the truly meshless local Petrov‐Galerkin (MLPG) method is established as a new paradigm in totally locking‐free computational analyses of shear flexible plates and shells.

This paper aims to introduce a new numerical approach based on the local weak form and the Petrov–Galerkin idea to numerically simulation of a predator–prey system with two-species, two chemicals and an additional chemotactic influence.

In the first proceeding, the space derivatives are discretized by using the direct meshless local Petrov–Galerkin method. This generates a nonlinear algebraic system of equations. The mentioned system is solved by using the Broyden’s method which this technique is not related to compute the Jacobian matrix.

This current work tries to bring forward a trustworthy and flexible numerical algorithm to simulate the system of predator–prey on the nonrectangular geometries.

The proposed numerical results confirm that the numerical procedure has acceptable results for the system of partial differential equations.

The purpose of this paper is to obtain accurate numerical solutions of two-dimensional (2-D) and 3-dimensional (3-D) Klein–Gordon–Schrödinger (KGS) equations.

The use of linear barycentric interpolation differentiation matrices facilitates the computation of numerical solutions both in 2-D and 3-D space within reasonable central processing unit times.

Numerical simulations corroborate the efficiency and accuracy of the proposed method.

Linear barycentric interpolation method is applied to 2-D and 3-D KGS equations for the first time, and good results are obtained.

The purpose of this paper is to present a new discretisation scheme, based on equation-coupled approach and high-order five-point integrated radial basis function (IRBF) approximations, for solving the first biharmonic equation, and its applications in fluid dynamics.

The first biharmonic equation, which can be defined in a rectangular or non-rectangular domain, is replaced by two Poisson equations. The field variables are approximated on overlapping local regions of only five grid points, where the IRBF approximations are constructed to include nodal values of not only the field variables but also their second-order derivatives and higher-order ones along the grid lines. In computing the Dirichlet boundary condition for an intermediate variable, the integration constants are used to incorporate the boundary values of the first-order derivative into the boundary IRBF approximation.

These proposed IRBF approximations on the stencil and on the boundary enable the boundary values of the derivative to be exactly imposed, and the IRBF solution to be much more accurate and not influenced much by the RBF width. The error is reduced at a rate that is much greater than four. In fluid dynamics applications, the method is able to capture well the structure of steady highly non-linear fluid flows using relatively coarse grids.

The main contribution of this study lies in the development of an effective high-order five-point stencil based on IRBFs for solving the first biharmonic equation in a coupled set of two Poisson equations. A fast rate of convergence (up to 11) is achieved.

This paper aims to present error compensation based on surface reconstruction to improve the positioning accuracy of industrial robots.

In previous research, it has been proved that the positioning error of industrial robots is continuous on the two-dimensional manifold of six-joint space. The point cloud generated by positioning error data can be used to fit the continuous surfaces, which makes it possible to apply surface reconstruction on error compensation. The moving least-squares interpolation and the B-spline method are used for the error surface reconstruction.

The results of experiments and simulations validate the effectiveness of error compensation by the moving least-squares interpolation and the B-spline method.

The proposed methods can control the average of compensated positioning error within 0.2 mm, which meets the requirement of a tolerance (±0.5 mm) for fastener hole drilling in aircraft assembly.

The error surface reconstruction based on the B-spline method has great superiority because fewer sample points are needed to use this method than others while keeping the compensation accuracy at the same level. The control points of the B-spline error surface can be adjusted with measured data, which can be applied for the error prediction in any temperature field.