A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling.The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex.For the temporal integration of the momentum equations,an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term.The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM).The momentum interpolation is used to damp out the spurious pressure wiggles.The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure.The classic test cases,the lid-driven cavity flow,the skew cavity flow and the backward-facing step flow,show that numerical results are in good agreement with the published benchmark solutions.     

A 3D pyramid spline element

In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate examples were employed to evaluate the performance of the proposed element.The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted,and it is comparable to the Lagrange element Q27.It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements.     

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.     

Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions(symmetric and non-symmetric)are studied in this work.Reliability of the obtained results is verified by the finite difference method(FDM)and the finite element method(FEM)with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes(regular and non-regular).The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.     

一种新的计算各向异性材料裂纹尖端应力强度因子杂交元法

利用有限元特征分析法研究了平面各向异性材料裂纹端部的奇性应力指数以及应力场和位移场的角分布函数,以此构造了一个新的裂纹尖端单元。文中利用该单元建立了研究裂纹尖端奇性场的杂交应力模型,并结合Hellinger-Reissner变分原理导出应力杂交元方程,建立了求解平面各向异性材料裂纹尖端问题的杂交元计算模型。与四节点单元相结合,由此提出了一种新的求解应力强度因子的杂交元法。最后给出了在平面应力和平面应变下求解裂纹尖端奇性场的算例。算例表明,本文所述方法不仅精度高,而且适应性强。     

Formulations of a hydromechanical interface element

A hydromechanical interface element is proposed for the consideration of the hydraulic-mechanical coupling effect along the interface.The fully coupled governing equations and the relevant finite element formulations are derived in detail for the interface element.All the involved matrices are of the same form as those of a solid element,which makes the incorporation of the model into a finite element program straightforward.Three examples are then numerically simulated using the interface element.Reasonable results confirm the correctness of the proposed model and motivate its application in hydromechanical contact problems in the future.     

弹性力学的杂交自然单元法

为了解决自然单元法无法直接求解节点应力以及应力解精度不高的问题, 将应力杂交的思想引入自然单元法中, 与弹性问题的Hellinger-Reissner变分原理结合, 提出了弹性问题的杂交自然单元法. 算例表明: 杂交自然单元法的计算结果与解析解吻合, 证明该方法是可行的; 在求解应力方面, 杂交自然单元法比自然单元法有着更高的计算精度, 而且可以直接求解出节点的应力.     

Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest’s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.     

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.     

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.     

A hybrid-stress element based on Hamilton principle

A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.     

APPLICATION OF PENALTY FUNCTION METHOD IN ISOPARANIETRIC HYBRID FINITE ELEMENT ANALYSIS

IntroductionSince T.H.H.Pain firstly puts forward hybrid element method[1]in1964, the researchand application of hybrid element have got great development. T.H.H.Painet al.havemade important pioneer works in the domain of the research on incompatible displacementstructure hybrid elementstress pattern[2,3]in recentdecades. Reference [4] had provided theoptimizing design concept of hybrid element further and established standardization methodof incompatible displacement structure hybrid eleme…     

Application of split Hopkinson tension bar technique to the study of dynamic fracture properties of materials

A novel approach is proposed in determining dynamic fracture toughness(DFT) of high strength steel,using the split Hopkinson tension bar(SHTB) apparatus,combined with a hybrid experimental-numerical method.The center-cracked tension specimen is connected between the bars with a specially designed fixture device.The fracture initiation time is measured by the strain gage method,and dynamic stress intensity factors(DSIF) are obtained with the aid of 3D finite element analysis(FEA).In this approach,the dimensions of the specimen are not restricted by the connection strength or the stress-state equilibrium conditions,and hence plane strain state can be attained conveniently at the crack tip.Through comparison between the obtained results and those in open publication,it is concluded that the experimental data are valid,and the method proposed here is reliable.The validity of the obtained DFT is checked with the ASTM criteria,and fracture surfaces are examined at the end of paper.     

Dynamic response of underground structures by time domain SBEM and SFEM

The dynamic interaction problems of three-dimensional linear elastic structures witharbitrary shaped section embedded in a homogeneous,isotropic and linear elastic half spaceunder dynamic disturbances are numerically solved.The numerical method employed is acombination of the time domain semi-analytical boundary element method(SBEM)usedfor the semi-infinite soil medium and the semi-analytical finite element method(SFEM)used for the three-dimensional structure.The two methods are combined throughequilibrium and compatibility conditions at the soil-structure interface.Displacements,velocities,accelerations and interaction forces at the interface between undergroundstructure and soil medium produced by the diffraction of wave by an underground structurefor every time step are obtained.In dynamic soil-structure interaction problems,it isadvantageous to combine the SBEM and the SFEM in an effort to produce an optimumnumerical hybrid scheme which is characterized by the main advantages of the two methods.The     

APPLICATION OF PENALTY FUNCTION METHOD IN ISOPARAMETRIC HYBRID FINITE ELEMENT ANALYSIS

By the aid of the penalty function method, the equilibrium restriction conditions were introduced to the isoparametric hybrid finite element analysis, and the concrete application course of the penalty function method in three-dimensional isoparametric hybrid finite element was discussed.The separated penalty parameters method and the optimal hybrid element model with penalty balance were also presented. The penalty balance method can effectively refrain the parasitical stress on the premise of no additional degrees of freedom. The numeric experiment shows that the presented element not only is effective in improving greatly the numeric calculation precision of distorted grids but also has the universality.     

含任意椭圆核各向异性板杂交应力有限元

基于含椭圆核有限大各向异性板弹性问题的复变函数级数解,应用杂交变分原理建立了一种与常规有限元相协调的含任意椭圆核各向异性板杂交应力有限元.单元内的应力场和位移场采用满足平衡方程、几何方程与物理方程的复变函数级数解,假设的复变函数级数解精确满足椭圆核边界处的位移协调条件和应力连续条件,单元外边界上的位移场按常规有限元位移场假设,单元内椭圆核的长轴可以与材料主轴不重合.单元刚度矩阵采用Gauss积分求得,并给出了建立刚度矩阵的主要公式和推倒过程.数值计算结果表明该单元具有计算精度高、计算工作量小等优点.     

周期分布多边形夹杂奇异性应力干涉问题的研究

采用一种新型的杂交元模型和一种单胞模型来解决周期分布多边形夹杂角部的奇异性应力相互干涉的问题。新型杂交元模型是基于广义Hellinger-Reissner变分原理建立的,其中奇异性应力场分量和位移场分量是采用有限元特征分析法的数值特征解得到的。使用当前的新型杂交元模型,只需要在夹杂角部邻域的周界上划分一维单元,避免了像传统有限元模型那样需要划分高密度二维单元。文中给出了代表奇异性应力场强度的夹杂角部广义应力强度因子数值解,并考虑材料属性、夹杂尺寸和夹杂位置关系的影响。算例中,考虑了夹杂和基体完全接合的情况,并给出了考核例。结果表明:当前模型能得到高精度数值解,且收敛性好;与传统有限元法和积分方程方法相比,该模型更具有通用性,为非均质材料的细观力学分析打下了基础。     

Element nodal computation-based radial integration BEM for non-homogeneous problems

This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial in-tegral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.     

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.     

Crack buckling in soft gels under compression

Recent interest in designing soft gels with high fracture toughness has called for simple and robust methods to test fracture behavior. The conventional method of applying tension to a gel sample suffers from a difficulty of sample gripping. In this paper, we study a possible fracture mechanism of soft gels under uni-axial compression. We show that the surfaces of a pre-existing crack, oriented parallel to the loading axis, can buckle at a critical compressive stress. This buckling instability can open the crack surfaces and create highly concentrated stress fields near the crack tip, which can lead to crack growth. We show that the onset of crack buckling can be deduced by a dimensional argument com- bined with an analysis to determine the critical compression needed to induce surface instabilities of an elastic half space. The critical compression for buckling was verified for a neo-Hookean material model using finite element simulations.