The smoothedfiniteelementmethod (S-FEM) has been found to be an effective solution method for solid mechanics problems. This paper proposes an effective approach to compute the lower bound solution of free vibratio...
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The smoothedfiniteelementmethod (S-FEM) has been found to be an effective solution method for solid mechanics problems. This paper proposes an effective approach to compute the lower bound solution of free vibration and the upper bound solution of the forced vibration of solid structures, by making use of the important softening effects of the node-based smoothed finite element method (NS-FEM). Through the gradient smoothing technique, the strain-displacement matrix is obtained in the smoothing domain based on the element mesh nodes. Subsequently, the stiffness matrix is computed in a manner consistent with the standard finiteelementmethod (FEM). Here, the practical Lanczos algorithm and the modal superposition technique are employed to obtain the frequencies, modes, and transient responses of a given homogeneous structure. For three-dimensional (3D) solid structures, the automatically generated four-node tetrahedron (T4) element meshes are utilized. The results obtained from the NS-FEM are compared with the standard FEM in terms of accuracy, convergence and computational efficiency.
This paper presents the node-based smoothed finite element method with linear strain functions (NS-FEM-L) for solving contact problems using triangular elements. The smoothed strains are formulated by a complete order...
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This paper presents the node-based smoothed finite element method with linear strain functions (NS-FEM-L) for solving contact problems using triangular elements. The smoothed strains are formulated by a complete order of polynomial functions and normalized with reference to the central points of smoothing domains. They are one order higher than those adopted in the finiteelementmethod (FEM) and the standard smoothedfiniteelementmethod with the same triangular mesh. When using linear functions to describe strains in smoothing domains, the solutions are more accurate and stable. The contact interfaces are discretized by contact point pairs using a modified Coulomb frictional contact model. The contact problems are solved via converting into linear complementarity problems (LCPs) which can be tackled by using the Lemke method. Numerical implementations are conducted to simulate the contact behavior, including the bonding-debonding, contacting-departing and sticking-slipping. The effects of various parameters related to friction and adhesion are intensively investigated. The comparison of numerical results produced by different methods demonstrates the validity and efficiency of the NS-FEM-L for contact problems.
Verification of the quantities of interest computed with the finiteelementmethod (FEM) requires an upper bound on the strain energy, which is half of the energy norm of displacement solutions. Recently, a modified f...
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Verification of the quantities of interest computed with the finiteelementmethod (FEM) requires an upper bound on the strain energy, which is half of the energy norm of displacement solutions. Recently, a modified finiteelementmethod with strain smoothing, the node-based smoothed finite element method (NS-FEM), has been proposed to solve solid mechanics problems. It has been found in some cases that the energy norm formed by the smoothed strain of NS-FEM solutions bounds the energy norm of exact displacements from above. We analyze the bounding property of this method, give three kind of energy norms of solutions computed by FEM and NS-FEM, and extend them to the computation of an upper bound and a lower bound on the linear functional of displacements. By examining the bounding property of NS-FEM with different energy norms using some linear elastic problems, the advantages of NS-FEM over the traditional error estimate basedmethods is observed. (C) 2014 Elsevier Ltd. All rights reserved.
In this paper, a four-node C0 tetrahedral element for the modified couple stress theory is proposed. Since the governing equations are the fourth-order differential equations, the first-order derivative of displacemen...
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In this paper, a four-node C0 tetrahedral element for the modified couple stress theory is proposed. Since the governing equations are the fourth-order differential equations, the first-order derivative of displacement or rotation should be approximated by a continuous function. In the proposed element, nodal rotations are defined using the node-based smoothing technique. Continuous rotation fields are defined with the shape functions and nodal rotations. Both the displacement field and the rotation field are expressed solely in terms of the displacement degrees of freedom. The element stiffness matrix is calculated using the newly defined rotation field. To prevent the increase of calculation cost due to increase of the bandwidth of the stiffness matrix, the preconditioned conjugate gradient method is introduced. The performance of the proposed element is evaluated through various numerical examples.
This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finiteelementmethod (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D ela...
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This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finiteelementmethod (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results.
A novel modelling approach for the electromagnetic forming process (EMF) is proposed in this paper. In the present work, a stable nodal integration method (SNIM) is used to calculate the electromagnetic field and an a...
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A novel modelling approach for the electromagnetic forming process (EMF) is proposed in this paper. In the present work, a stable nodal integration method (SNIM) is used to calculate the electromagnetic field and an axisymmetric thin shell element is firstly employed for mechanical field analysis to improve the computational efficiency. A layered approach is adopted to predict the gradual spread of plasticity in a shell. To solve the coupled electromagnetic-mechanical problem, a mapping rule is developed to transfer the nodal Lorentz force from the electromagnetic field to the mechanical field. Simultaneously, a solid element with the finiteelementmethod (FEM) is employed in the mechanical field for comparison to validate the efficiency of the proposed modelling approach;the FEM is customarily adopted in a conventional numerical method of EMF simulation. Several electromagnetic forming examples are presented to demonstrate the applicability of the proposed model for EMF problems, and the model is validated by comparing its results with available experimental results in the literature. The numerical results obtained by the proposed model are in good accordance with the experiments and show that the proposed model has much lower computational costs than the conventional one. (C) 2017 Elsevier B.V. All rights reserved.
A stable nodal integration method (SNIM) is presented to solve static and quasi-static electromagnetic problems in this paper. The analysis domain is firstly discretized into a set of triangular or tetrahedral element...
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A stable nodal integration method (SNIM) is presented to solve static and quasi-static electromagnetic problems in this paper. The analysis domain is firstly discretized into a set of triangular or tetrahedral elements, and linear interpolation is adopted within each element. A weakened weak formulation based on the nodes is further considered, framing the so-called node-based smoothing domains. Equivalent smoothing domains are then acquired as circular or spherical regions, where the gradient of shape function is expanded as the first order Taylor form. Subsequently, four or six temporary integration points on the region are picked to obtain items of the stiffness matrix and the external load vector. By simplifying the equations, the stiffness matrix can be received in quite concise form with one point integration and stabilization terms, which are calculated on original nodebased smoothing domains. The implementation of SNIM on electromagnetic problems is thus realized. The proposed formulation is validated against both analytical solutions and traditional methods, and its effectiveness and potentialities can be well represented and clarified by numerical examples. (C) 2017 Elsevier Inc. All rights reserved.
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