An efficient meshless collocation method for the analysis of two-dimensional piezoelectric structures

Despite of the fact that in the title the analysis of two-dimensional structures is indicated, we shall be concerned with three-dimensional structures made from composite non-homogeneus anisotropic linear visco-elastic materials. The problem considered is a quasi-static one in which inertia forces due to deformation could be neglected.

The isogeometric analysis (IGA) that integrates Computer Aided Design(CAD) and Computer Aided Engineering (CAE) is found so far the effectively numerical tool for the analysis of a variety of practical problems. In this paper, we develop further the NURBS based isogeometric analysis framework for piezoelectric structures.The method employs the NURBS basis functions in both geometry representation and analysis. The main advantages of the present method are capable of handling the exactgeometry of conic sections and making the flexibility of refinement and degree elevationwith an arbitrary continuity of basic functions. These features results in high accuracy of approximate solutions for practical applications, especially piezoelectric problems. Three numerical examples are provided to validate excellent performance of the present method.

We investigate two-dimensional cluster structures composed of ferromagnetic colloidal particles, based on a flexible chain model, by the configurational-bias Monte Carlo method. We clarify the dependence of the probabilities of the creation of different types of clusters on the dipole-dipole interactive energy and the cluster size.

In this paper, the boundary element method (BEM) based on elasticity theory is developed for two-dimensional (2-D) thin structures with the thickness to length ratio in the micro (10−6) or nano (10−9) scales. An efficient analytical method is developed to deal with the nearly-singular integrals in the boundary integral equation (BIE) for 2-D thin structures. The nearly-singular integrals, which are line integrals for 2-D problems and arise when two boundary curves are close to each other, are transformed into function evaluations at the two end points of the element of integration. In addition, a new nonlinear coordinate transformation is developed for nearly weakly-singular integrals to further increase the numerical accuracy. For the test problems studied, very promising results are obtained when the thickness to length ratio is in the orders of 10−6 to 10−9, which is sufficient for modeling most thin structures in the micro- or nano-scales. The developed method can be applied readily to model layered coatings, thin films or other layered structures to analyze contact stresses, interfacial cracks, thermal effects and nonlinear deformations.

In this study, a receptivity analysis of streaks, oblique and two-dimensional flow structures is presented with a stochastic receptivity framework for different inputs for supersonic adiabatic boundary layer flows. In particular, an active role of temperature fluctuation is identified for the amplification of oblique patterns, while a passive role is observed for the onset of streaks and two-dimensional flow structures. From a practical point of view, this study can help to improve the effectiveness of actuators aiming at a particular response in supersonic boundary layer flows.

Tile vaults as integrated formwork for reinforced concrete: Construction, experimental testing and a method for the design and analysis of two-dimensional structures

Simulation analysis of III-N two-dimensional electron gas-based structures that could be used for stable monolithically integrated enhancement/depletion-mode circuits was carried out. Three different designs were proposed and analysed, including a novel p-GaN/AlN-GaN SPSL/GaN, which is expected to have lower ON-state resistance and higher transconductance than conventional normally-off GaN-based transistors.

A general constraint-based formulation for the analysis and partial synthesis of two-dimensional truss structures is presented. This formulation is general in that it handles statically determinate and statically indeterminate trusses with pin and roller supports, and concentrated joint loads. The formulation is constraint-based in that the physical behavior of truss components is declaratively represented using constraints.The analysis and partial synthesis of a truss structure manifest themselves in proving the satisfiability of the constraints associated with the structural components. An artificial intelligence approach called constraint logic programming is used for representing and satisfying constraints. A constraint logic programming language, called CLP(R), is used for implementing the formulation. The implemented program consists of sixteen rules. These rules are used for both the analysis and partial synthesis of truss structures. Several truss analysis and synthesis examples using the formulation are presented.

Based on previous findings concerning the numerical solution of one-dimensional elastodynamical problems [Provatidis in Arch Appl Mech 78(4):241–250, 2008] this paper extends the methodology to the static analysis of two-dimensional problems in quadrilateral domains. This target is achieved by replacing the Galerkin/Ritz procedure involved in Lagrangian (or Gordon–Coons) type finite elements by a global collocation scheme. In brief, the boundary conditions are fulfilled at all boundary nodes, while the governing equation is fulfilled at internal points. The theory is supported by four test cases concerning rectangular and curvilinear structures under plane-stress or plane-strain conditions, where the convergence rate is successfully compared with that of conventional bilinear finite elements with the same mesh density.

RMVT-based meshless collocation and element-free Galerkin methods for the approximate 3D analysis of multilayered composite and FGM circular hollow cylinders

A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory

In the present work, the nonlinear static analysis of functionally graded hyperelastic thin plate is investigated. The neo‐Hookean strain energy function and right Cauchy‐Green tensor are utilized to formulate the potential energy function. Also, the first‐order shear deformation theory of the plate is used to form the strain‐displacement relations. The strong form of the governing equations is derived using Euler‐Lagrange relations, and these relations are discretized using the meshless collocation method (MCM). The thin‐plate spline (TPS) radial basis function (RBF) is utilized to discretize the nonlinear governing equations, and the arc‐length continuation algorithm is used to solve the nonlinear algebraic system of equations. Square and circular plates with clamped and simply supported boundary conditions and various power‐law indexes are investigated using the MCM. The results are compared to those of the finite element method (FEM). The results show that the MCM is an accurate and efficient method in comparison to FEM for circular and square functionally graded (FG) hyperelastic thin plates.

Hamiltonian Approach to Piezoelectric Fracture

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.

This paper considered the spectral meshless radial point interpolation (SMRPI) method to unravel for the nonlinear p-Laplacian equation with mixed Dirichlet and Neumann boundary conditions. Through this assessment, which includes meshless methods and collocation techniques based on radial point interpolation, we construct the shape functions, with the Kronecker delta function property, as basis functions in the framework of spectral collocation methods. Studies in this regard require one to evaluate the high-order derivatives without any kind of integration locally over the small quadrature domains. Finally, some examples are given to illustrate the low computing costs and high enough accuracy and efficiency of this method to solve a p-Laplacian equation and it would be of great help to fulfill the implementation related to the element-free Galerkin (EFG) method. Both the SMRPI and the EFG methods have been compared by similar numerical examples to show their application in strongly nonlinear problems.