An overview of layerwise theories for composite laminates and structures: Development, numerical implementation and application

The meshfree methods in computational mechanics have been actively proposed and increasingly developed in order to overcome some drawbacks in the conventional numerical methods. Over past three decades meshfree methods have found their way into many different application areas ranging from classical astronomical problems to solid mechanics analysis, fluid flow problems, vibration analysis, heat transfer and optimization to the numerical solution of all kind of (partial) differential equation problems. The present work is an effort to provide a comprehensive review of various Meshfree methods, their classification, underlying methodology, application area along with their advantages and limitations. Key contributions of mesh free techniques to the area of fracture mechanics have been discussed with applications of element free Galerkin method (EFGM) to fracture analysis as primary concern.

Meshfree Methods: A Comprehensive Review of Applications

In this paper, a relaxed Hermitian and skew-Hermitian splitting (RHSS) preconditioner is proposed for saddle point problems from the element-free Galerkin (EFG) discretization method. The EFG method is one of the most widely used meshfree methods for solving partial differential equations. The RHSS preconditioner is constructed much closer to the coefficient matrix than the well-known HSS preconditioner, r in a RHSS fixed-point iteration. Convergence of the RHSS iteration is analyzed and an optimal parameter, which minimizes the spectral radius of the iteration matrix is described. Using the RHSS preconditioner to accelerate the convergence of some Krylov subspace methods (like GMRES) is also studied. Theoretical analyses show that the eigenvalues of the RHSS preconditioned matrix are real and located in a positive interval. Eigenvector distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are obtained. A practical parameter is suggested in implementing the RHSS preconditioner. Finally, some numerical experiments are illustrated to show the effectiveness of the new preconditioner.

A relaxed hss preconditioner for saddle point problems from meshfree discretization

The numerical analysis of piezoelectric ceramics based on the Hermite-type RPIM

The research progress of a novel traffic solution, a submerged floating tunnel (SFT), is reviewed in terms of a study approach and loading scenario. Among existing publications, the buoyancy–weight ratio (BWR) is usually predefined. However, BWR is a critical structural parameter that tremendously affects the dynamic behaviour of not only the tunnel tube itself but also the cable system. In the context of a SFT prototype (SFTP) project in Qiandao Lake (Zhejiang Province, China), the importance of BWR is illustrated by finite element analysis and subsequently, an optimized BWR is proposed within a reasonable range in the present study. In the numerical model, structural damping is identified to be of importance. Rayleigh damping and the corresponding Rayleigh coefficients are attained through a sensitivity study, which shows that the adopted damping ratios are fairly suitable for SFTP. Lastly, the human sense of security is considered by quantifying the comfort index, which helps further optimize BWR in the SFTP structural parameter design. Submerged floating tunnel is a novel traffic solution. In the prototype project in Qiandao Lake, the importance of buoyancy–weight ratio (BWR) is illustrated. Subsequently, BWR of 1.2 could be the most promising choice based on dynamic responses and human senses of security and comfort.

Feasibility study on buoyancy-weight ratios of a submerged floating tunnel prototype subjected to hydrodynamic loads

New treatment of essential boundary conditions in EFG method by coupling with RPIM

A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares (MLS) approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only displacement degrees of freedom (d.o.f.s), is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.

A 3D shell-like approach using element-free Galerkin method for analysis of thin and thick plate structures

Piezoelectric laminated beams are common piezoelectric structure. It has been applied in many fields, such as the driving element of the bimorph and unimorph piezoelectric actuators bending. For static and dynamic, linear and nonlinear, analytical method and numerical method, the mechanical behaviors of this structure (including bending, vibration, buckling and control, etc.) have very comprehensive research. In these studies, most of the research is to use of laminated beam theory simplified into 1D control equation. However, this paper will adopt a new approximate method based on 2D element free Galerkin (2D-EFG) for the numerical simulation of piezoelectric laminated Timoshenko beam bending. This new meshless method can overcome the material discontinuity between layer and thickness lock phenomenon. This new method is suitable for thin beam and thick beam. It can be generalized to the numerical calculation of laminated curved beam, laminated plate and shell structures. Numerical examples verify the validity and precision of the proposed method.

A new meshless method based on 2D-EFG for the analysis of piezoelectric laminated Timoshenko beam

In this paper, a new formulation of piezoelectric laminated plates based on the linear piezoelectricity theory and the layerwise theory is developed. The linear piezoelectricity theory focuses on the coupling between mechanical deformations and the charge equations of electrostatics. The layerwise theory is used for the mechanical displacement field and the potential function. The equations of motion and boundary conditions are developed using an energy principle. A meshless collocation method based on the radial basis function is used to discrete the system equations. The proposed approach is good in that it can reflect the laminar stress effect, produce exactly electromechanical behaviors and accommodate multiple voltage inputs or outputs. Numerical examples verify the validity and precision of the proposed method.

Yu Yin

Papers

New treatment of essential boundary conditions in EFG method by coupling with RPIM

A 3D shell-like approach using element-free Galerkin method for analysis of thin and thick plate structures

A new meshless method based on 2D-EFG for the analysis of piezoelectric laminated Timoshenko beam

Analysis of piezoelectric laminated plates using the layerwise plate theory and radial basis function collocation method

Prediction method for shear stability of composite hat-stringer stiffened panel