Finite Element Element-free Galerkin Research Articles

Solving linear elasticity benchmark problems via the overset improved element-free Galerkin-finite element method

A novel approach for the solution of linear elasticity problems is introduced in this communication, which uses a hybrid chimera-type technique based on both finite element and improved element-free Galerkin methods. The proposed overset improved element-free Galerkin-finite element method (Ov-IEFG-FEM) for linear elasticity uses the finite element method (FEM) throughout the entire problem geometry, whereas a fine distribution of overlapping nodes is used to perform higher order approximations via the improved element-free Galerkin (IEFG) technique in regions demanding more computational accuracy. The method relies on keeping the FEM-based results in those regions where low order of approximation is enough to provide the required accuracy, i.e. outside the region where the solution will be enriched via the IEFG technique. The overlapping domains perform an iterative transfer of kinematics information through well-defined immersed boundaries, and a detailed explanation on this regard is also presented in this communication. The Ov-IEFG-FEM is used in a set of increasingly complex linear elasticity problems, and the outcomes demonstrate the suitability and reliability of this technique to solve such problems in an accurate and remarkably simple manner.

An overset improved element-free Galerkin-finite element method for the solution of transient heat conduction problems with concentrated moving heat sources

A novel Overset Improved Element-Free Galerkin-Finite Element Method (Ov-IEFG-FEM) for solving transient heat conduction problems with concentrated moving heat sources is introduced in this communication. The method is a mesh-less/mesh-based chimera-type approach that utilises a coarse finite element mesh to discretise the problem geometry, while a separate set of overlapping nodes (patch nodes) moves with the heat source to capture the marked thermal gradients with higher accuracy using the Improved Element-Free Galerkin (IEFG) technique. Outside of the heat source area, where accuracy requirements are significantly lower, the thermal problem is solved using the Finite Element Method (FEM). The approach involves solving the problem over these two overlapping computational domains and transferring numerical information between the approximations performed on both. Such transfer of information occurs through immersed boundaries that are properly defined, enabling straightforward achievement of accurate results. The proposed Ov-IEFG-FEM is conceived to provide an enriched solution by appropriately coupling the temperature fields computed on the patch nodes and the coarse background mesh using IEFG and FEM, respectively. A comprehensive explanation concerning the appropriate coupling between the temperature fields of both the coarse background finite element mesh and the fine arrangement of moving patch nodes for the IEFG computations, is also provided in this communication. Numerical experiments demonstrate the method effectiveness in accurately and efficiently solving transient heat conduction problems with concentrated moving heat sources.

Rheological experimental properties and numerical modeling of a pressure-transmitting silicone rubber used in sheet metal flexible-die forming

In this paper, the rheological behaviors of a silicone rubber used in sheet metal flexible-die forming were analyzed experimentally and numerically. Firstly, six silicone rubber samples with different molecular weights were subjected to three tests: oscillation, creep recovery, and shear viscosity test by using dynamic shear rheometer (DSR). Then, the responses of the silicone rubber to the load were categorized into three groups as elasticity, viscoelasticity, and viscoplasticity depending on whether they were time dependent and recoverable during the unloading period. By applying Perzyna’s theory, a visco-elasto-plastic model was proposed to simulate the rheological behaviors of the silicone rubber numerically. Finally, a finite element-element-free Galerkin (FE-EFG) code was implemented on the basis of this numerical model. Employing the program into polymer extrusion and sheet metal flexible-die forming process, on the substation of parameters obtained from experiments, good matches were found between numerical results and experimental ones.

EIT image reconstruction based on a hybrid FE-EFG forward method and the complete-electrode model

This paper presents the application of the hybrid finite element–element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and the EFG method is computationally expensive. In this paper, the hybrid FE-EFG method is applied to take both advantages of FE and EFG methods, the complete electrode model of the forward problem is solved, and an iterative regularized Gauss–Newton method is adopted to solve the inverse problem. The proposed method is applied to compute Jacobian in the inverse problem. Utilizing 2D circular homogenous models, the numerical results are validated with analytical and experimental results and the performance of the hybrid FE-EFG method compared with the FE method is illustrated. Results of image reconstruction are presented for a human chest experimental phantom.

Evaluation of mechanical properties using spherical ball indentation and coupled finite element–element-free galerkin approach

ABSTRACTIn the present work, the mechanical properties of pressure tube material (Zr-Nb2.5) are evaluated using the coupled finite element–element-free Galerkin approach. Penalty approach is used to impose contact constraints and non-penetration condition at the interface. An efficient node-to-segment algorithm is employed to model the contact behavior. An updated Lagrangian approach is used to model the large deformation. Loading and unloading response of the indentation process is analyzed using von-Mises and Gurson-Tvergaard-Needleman (GTN) plasticity models. In multiple indentations, the indentation depth is progressively increased up to a maximum specified limit with partial unloading. Load-indentation depth curves are used to extract the flow properties of the material.

An adaptive EFG-FE coupling method for elasto-plastic contact of rough surfaces

Differing from Finite Element Method, the meshless method does not need any mesh information and can arrange nodes freely which is perfectly suitable for adaptive analysis. In order to simulate the contact condition factually and improve computational efficiency, an adaptive procedure for Element-free Galerkin-Finite Element (EFG-FE) coupling contact model is established and developed to investigate the elastoplastic contact performance for engineering rough surfaces. The local adaptive refinement strategy combined with the strain energy gradient-based error estimation model is employed. The schemes, including principle explanation, arithmetic analysis and programming realization, are introduced and discussed. Furthermore, some related parameters on adaptive convergence criterion are researched emphatically, including adaptation-stop criterion, refinement or coarsening criterion which are guided by the relative error in total strain energy with two adjacent stages. Based on pioneering works of the EFG-FE coupling method for contact problems, an adaptive EFG-FE model for asperity contact is studied. Compared with the solutions obtained from the uniform refinement model, the adaptation results indicate that the adaptive method presented in this paper is capable of solving asperity contact problems with excellent calculation accuracy and computational efficiency.

Adaptive finite element-element-free Galerkin coupling method for bulk metal forming processes

An adaptive finite element-element-free Galerkin (FE-EFG) coupling method is proposed and developed for the numerical simulation of bulk metal forming processes. This approach is able to adaptively convert distorted FE elements to EFG domain in analysis. A new scheme to implement adaptive conversion and coupling is presented. The coupling method takes both advantages of finite element method (FEM) and meshless methods. It is capable of handling large deformations with no need of remeshing procedures, while it is computationally more efficient than those full meshless methods. The effectiveness of the proposed method is demonstrated with the numerical simulations of the bulk metal forming processes including forging and extrusion.

Sensitivity analysis and shape optimization based on FE–EFG coupled method

By use of 4-node isoparametric quadrangle interface element between finite element (FE) and meshless regions, a collocation approach is introduced to couple firstly FE and element-free Galerkin (EFG) method in this paper. By taking derivative of discreteness equilibrium equation at interface element with respect to design variable, a numerical method for discreteness-based shape design sensitivity analysis in interface element is obtained. The design sensitivity analysis (DSA) of coupled FE–EFG method is achieved by employing the DSA of nodal displacement at the interface element. The numerical method presented is testified by examples. It can be observed excellent agreement between the numerical results and the analytical solution. Finally the shape optimization of fillet is achieved by using coupled FE–EFG method. The result obtained show that imposing of the essential boundary condition is easy to implement, the computational time is reduced and the distortion of mesh is avoided.

AN ADAPTIVE MESHLESS COMPUTATIONAL SYSTEM FOR ELASTOPLASTIC CONTACT PROBLEMS

An adaptive meshless computational system is introduced in this paper to solve two-dimensional elastoplastic contact mechanics. An adaptive element-free Galerkin-finite element coupling computational model based on the gradient of strain energy and a linear programming technique with the initial stiffness method for elastoplastic contact problems are combined. Principle explanation and program realization are carried out. The modularization concept in software engineering is used, and the adaptive change of the influence domain radius and the elastoplastic property of material are also taken into account by the system. A rigid cylinder making contact with an elastic plane is analyzed to validate the system. Some key parameters in adaptive calculation are studied. The adaptive meshless computational system is also applied to elastoplastic contact of rough surfaces. Comparisons of the adaptive refinement solution with the uniform refinement solution are made, and the results show the satisfactory accuracy and efficiency of the solutions from the adaptive refinement model.

An Adaptive EFG-FE Computational Model for Thermal Elasto-Plastic Frictional Contact Problems

An adaptive meshless element-free Galerkin-finite element (EFG-FE) coupling model for thermal elasto-plastic contact problems is developed to investigate the influences of the steady-state frictional heating on the contact performance of two contacting bodies. The thermal elasto-plastic contact problems using the initial stiffness method is presented. The local adaptive refinement strategy and the strain energy gradient-based error estimation for EFG-FE coupling method are combined. The adaptive meshless model takes into account the temperature variation, micro plastic flow, and the coupled thermo-elasto-plastic behavior of the materials, considering the strain-hardening property of the materials and temperature-dependent yield strength. The adaptive model is verified through the contact analysis of a cylinder with an elasto-plastic plane. The thermal effects on the contact pressure, stresses distributions with certain frictional heat inputs are studied. The results show that the accuracy of the solutions from the adaptive refinement model is satisfactory but the cost of the CPU time is much less than that for the uniform refinement calculation.

Two-Dimensional Adaptive-Surface Elasto-Plastic Asperity Contact Model

When contact problems are solved by numerical approaches, a surface profile is usually described by a series of discrete nodes with the same intervals along a coordinate axis. Contact computation based on roughness datum mesh may be time consuming. An adaptive-surface elasto-plastic asperity contact model is presented in this paper. Such a model is developed in order to reduce the computing time by removing the surface nodes that have little influence on the contact behavior of rough surfaces. The nodes to be removed are determined by a prescribed threshold. The adaptive-surface asperity contact model is solved by means of the element-free Galerkin-finite element coupling method because of its flexibility in domain discretization and versatility in node arrangements. The effects of different thresholds on contact pressure distribution, real contact area, and elasto-plastic stress fields in contacting bodies are investigated and discussed. The results show that this model can help reduce about 48% computational time when the relative errors are about 5%.

An Element-Free Galerkin-Finite Element Coupling Method for Elasto-Plastic Contact Problems

The element-free Galerkin-finite element (EFG-FE) coupling method, combined with the linear mathematical programming technique, is utilized to solve two-dimensional elasto-plastic contact problems. Two discretized models for an elastic cylinder contacting with a rigid plane are used to investigate the boundary effects in a contact problem when using the EFG-FE coupling method under symmetric conditions. The influences of the number of Gauss integration points and the size supporting the weight function in the meshless region on the contact pressure and stress distributions are studied and discussed by comparing the numerical results with the theoretical ones. Furthermore, the elasto-plastic contact problems of a smooth cylinder with a plane and a rough surface with a plane are analyzed by means of the EFG-FE method and different elasto-plasticity models.

An EFG-FE Coupling Method for Microscale Adhesive Contacts

An elastic adhesive contact model based on the element-free Galerkin-finite element (EFG-FE) coupling method is presented in this paper. The model is first validated though comparison to theoretical solutions. A numerical simulation of the adhesive contact between a microelastic cylinder and a rigid half-space is then conducted. The adhesive contact characteristics of three metals (Al, Cu, and Fe) are studied at different Tabor parameters. The relationships of the applied load and contact half-width of the adhesive contacts are analyzed. Contact pressures, stress contours and deformed profiles of different cylinder sizes and applied loads are illustrated and discussed. The results are compared to published solutions, and good agreements are observed.

Hybrid element-free Galerkin-finite element method for electromagnetic field computations

A new hybrid computational procedure utilizing the Element-free Galerkin method (EFGM) and the finite element method (FEM) for electromagnetic field computations is proposed. With the proposed method, only a part of the analyzed domain is modeled using the EFGM, while the rest of the analysis domain is discretized using the ordinary FEM. The connection between both subdomains is enabled using an intermediate analysis subdomain where new hybrid shape functions are defined utilizing both EFGM and FEM shape functions as bases. The accuracy of the obtained results by the proposed method is of the same order with those obtained by the ordinary FEM, but with less computation effort.