An algebraic multigrid solver for finite element computations in solid mechanics

1997 ◽  
Vol 14 (2) ◽  
pp. 202-215 ◽  
Author(s):  
A. Boersma ◽  
P. Wriggers
2014 ◽  
Vol 15 (4) ◽  
pp. 1045-1067 ◽  
Author(s):  
Wenqiang Feng ◽  
Xiaoming He ◽  
Yanping Lin ◽  
Xu Zhang

AbstractThis article is to discuss the bilinear and linear immersed finite element (IFE) solutions generated from the algebraic multigrid solver for both stationary and moving interface problems. For the numerical methods based on finite difference formulation and a structured mesh independent of the interface, the stiffness matrix of the linear system is usually not symmetric positive-definite, which demands extra efforts to design efficient multigrid methods. On the other hand, the stiffness matrix arising from the IFE methods are naturally symmetric positive-definite. Hence the IFE-AMG algorithm is proposed to solve the linear systems of the bilinear and linear IFE methods for both stationary and moving interface problems. The numerical examples demonstrate the features of the proposed algorithms, including the optimal convergence in both L2and semi-H1norms of the IFE-AMG solutions, the high efficiency with proper choice of the components and parameters of AMG, the influence of the tolerance and the smoother type of AMG on the convergence of the IFE solutions for the interface problems, and the relationship between the cost and the moving interface location.


2015 ◽  
Vol 07 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Z. C. He ◽  
G. Y. Zhang ◽  
L. Deng ◽  
Eric Li ◽  
G. R. Liu

The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.


Author(s):  
K. S. Al-Athel ◽  
M. S. Gadala

The adaptation of the volume of fluid method (VOF) to solid mechanics (VOS) is presented in this work with the focus on metal forming applications. The method is discussed for a general non-uniform mesh with Eulerian finite element formulation. The implementation of the VOS method in metal forming applications is presented by focusing on topics such as the contact between the tool and the workpiece, tracking of the free surface of the material flow and the connectivity of the free surface during the whole process. Improvement on the connectivity of the free surface and the representation of curves is achieved by considering the mechanics of different metal forming processes. Different applications are simulated and discussed to highlight the capability of the VOS method.


2000 ◽  
Vol 123 (1) ◽  
pp. 150-154
Author(s):  
John H. Underwood ◽  
Michael J. Glennon

Laboratory fatigue life results are summarized from several test series of high-strength steel cannon breech closure assemblies pressurized by rapid application of hydraulic oil. The tests were performed to determine safe fatigue lives of high-pressure components at the breech end of the cannon and breech assembly. Careful reanalysis of the fatigue life tests provides data for stress and fatigue life models for breech components, over the following ranges of key parameters: 380–745 MPa cyclic internal pressure; 100–160 mm bore diameter cannon pressure vessels; 1040–1170 MPa yield strength A723 steel; no residual stress, shot peen residual stress, overload residual stress. Modeling of applied and residual stresses at the location of the fatigue failure site is performed by elastic-plastic finite element analysis using ABAQUS and by solid mechanics analysis. Shot peen and overload residual stresses are modeled by superposing typical or calculated residual stress distributions on the applied stresses. Overload residual stresses are obtained directly from the finite element model of the breech, with the breech overload applied to the model in the same way as with actual components. Modeling of the fatigue life of the components is based on the fatigue intensity factor concept of Underwood and Parker, a fracture mechanics description of life that accounts for residual stresses, material yield strength and initial defect size. The fatigue life model describes six test conditions in a stress versus life plot with an R2 correlation of 0.94, and shows significantly lower correlation when known variations in yield strength, stress concentration factor, or residual stress are not included in the model input, thus demonstrating the model sensitivity to these variables.


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