An immersed boundary element method for level‐set based topology optimization

In this paper, we propose a new BEM for level‐set based topology optimization. In the proposed BEM, the nodal coordinates of the boundary element are replaced with the nodal level‐set function and the nodal coordinates of the Eulerian mesh that maintains the level‐set function. Because this replacement causes the nodal coordinates of the boundary element to disappear, the boundary element mesh appears to be immersed in the Eulerian mesh. Therefore, we call the proposed BEM an immersed BEM. The relationship between the nodal coordinates of the boundary element and the nodal level‐set function of the Eulerian mesh is clearly represented, and therefore, the sensitivities with respect to the nodal level‐set function are strictly derived in the immersed BEM. Furthermore, the immersed BEM completely eliminates grayscale elements that are known to cause numerical difficulties in topology optimization. By using the immersed BEM, we construct a concrete topology optimization method for solving the minimum compliance problem. We provide some numerical examples and discuss the usefulness of the constructed optimization method on the basis of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.     

大型多支承回转窑托轮偏斜接触有限元分析

针对回转窑托轮偏斜对接触区应力分布的影响,运用赫兹接触理论,推导出托轮与滚圈最大接触应力比与托轮偏斜角的关系;采用有限元方法计算某支承结构托轮平行与呈最大偏斜角时的接触问题,得到支承部件接触应力和等效应力应变分布情况,并得出滚圈和托轮的危险易损部位;为回转窑的轴向调控提供了有效的理论依据。     

广义逆特征值方法在动力模型修正中的应用

本文针对土木工程中理论计算的要求和特点,基于逆特征值理论给出了一种适合有限元动力模型修正的广义逆特征值方法,该方法在给出修正解的表达式基础上,要求修正解满足动力模型的力学特征,且仅需要少量试验数据,是一种简单、实用的有限元模型修正方法。     

无应力奇异性条件下的界面应力集中问题研究

应用有限元分析技术,对无应力奇异性条件下的双材料粘接接头的应力集中问题进行了数值研究。首先,根据特征方程分析求解出消除接头界面端和界面角奇异应力场的材料组合和几何条件;据此提出了几种无应力奇异性影响并且为宏观等截面的双材料粘接接头几何模型。然后在轴对称假设条件下,对上述模型理想粘接界面上的应力分布进行了分析,着重讨论了材料组合和界面几何形状对这些应力大小的影响。结果表明:由于材料性能错配,界面上的应力集中现象不可避免,其大小依赖于材料组合和界面几何形状。这些分析结果对于指导界面几何形状优化设计,最终提高界面强度具有一定的参考价值。     

Fracture and fragmentation of simplicial finite element meshes using graphs

An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the three‐dimensional fracture algorithm by Pandolfi and Ortiz (Eng. Comput. 1998; 14 (4):287–308). It is shown that the graph representation initializes in O(N) time and fractures in O(N) time, while the reference implementation requires O(N) time to initialize and O(N) time to fracture, where N_E is the number of elements in the mesh and N_I is the number of interfaces to fracture. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of singular stress fields at multi‐material corners under thermal loading

The scaled boundary finite‐element method is extended to the modelling of thermal stresses. The particular solution for the non‐homogeneous term caused by thermal loading is expressed as integrals in the radial direction, which are evaluated analytically for temperature changes varying as power functions of the radial coordinate. When applied to model a multi‐material corner, only the boundary of the problem domain is discretized. The boundary conditions on the straight material interfaces and the side‐faces forming the corner are satisfied analytically without discretization. The stress field is expressed semi‐analytically as a series solution. The stress distribution along the radial direction, including both the real and complex power singularity and the power‐logarithmic singularity, is represented analytically. The stress intensity factors are determined directly from their definitions in stresses. No knowledge on asymptotic expansions is required. Numerical examples are calculated to evaluate the accuracy of the scaled boundary finite‐element method. Copyright © 2005 John Wiley & Sons, Ltd.     

塑性大变形有限元静水压力的改进算法

本文针对塑性大变形有限元中静水压力计算精度低的问题,研究了三维八节点等参元的偏应力导数佳点,提出了一种改进的静水压力间接积分算法。将该算法应用于金属塑性成型过程的有限元模拟,较好地解决了大步长情况下应力计算精度低的问题。     

A super‐element for crack analysis in the time domain

A super‐element for the dynamic analysis of two‐dimensional crack problems is developed based on the scaled boundary finite‐element method. The boundary of the super‐element containing a crack tip is discretized with line elements. The governing partial differential equations formulated in the scaled boundary co‐ordinates are transformed to ordinary differential equations in the frequency domain by applying the Galerkin's weighted residual technique. The displacements in the radial direction from the crack tip to a point on the boundary are solved analytically without any a priori assumption. The scaled boundary finite‐element formulation leads to symmetric static stiffness and mass matrices. The super‐element can be coupled seamlessly with standard finite elements. The transient response is evaluated directly in the time domain using a standard time‐integration scheme. The stress field, including the singularity around the crack tip, is expressed semi‐analytically. The stress intensity factors are evaluated without directly addressing singular functions, as the limit in their definitions is performed analytically. Copyright © 2004 John Wiley & Sons, Ltd.     

A dual mortar approach for 3D finite deformation contact with consistent linearization

In this paper, an approach for three‐dimensional frictionless contact based on a dual mortar formulation and using a primal–dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two‐dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi‐smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Quasi-optimal Tikhonov penalization and parameterization coarseness in space-dependent function estimation

The determination of space-dependent functions from boundary measurements or inner pointwise measurements is ill-posed inverse problems that require regularization tools to be stabilized. Among numerous regularization strategies, the Tikhonov penalization is one of the most used in the field of space-dependent function estimation. Its efficient use relies on the Tikhonov parameter value for which search is time consuming although necessary, especially in the field of nonlinear inversion. Other strategies, such as appropriate parameterization, have recently proven to be very efficient to cope with the ill-posedness of such problems. This paper shows that the optimal Tikhonov parameter is almost independent of the mesh used to project the functions to be retrieved. As a consequence, this value should be seeked using a coarse mesh even though reconstructions could further be done on finer meshes. This conclusion is validated by numerical means.     

Combined interior‐point method and semismooth Newton method for frictionless contact problems

In the present paper, a solution scheme is proposed for frictionless contact problems of linear elastic bodies, which are discretized using the finite element method with lower order elements. An approach combining the interior‐point method and the semismooth Newton method is proposed. In this method, an initial active set for the semismooth Newton method is obtained from the approximate optimal solution by the interior‐point method. The simplest node‐to‐node contact model is considered in the present paper, that is, pairs of matching nodes exist on the contact surfaces. However, the discussions can be easily extended to a node‐to‐segment or segment‐to‐segment contact model. In order to evaluate the proposed method, a number of illustrative examples of the frictionless contact problem are shown. The proposed combined method is compared with the interior‐point method and the semismooth Newton method. Two numerical examples that are difficult to solve using the semismooth Newton method are solved effectively using the proposed combined method. It is shown that the proposed method converges within far fewer iterations than the semismooth Newton methods or the interior‐point method. Copyright © 2009 John Wiley & Sons, Ltd.