高度不规则网格多边形单元的有理函数插值格式

借鉴自然邻点插值法,提出了基于高度不规则网格多边形单元的有理函数插值格式一多边形有理函数插值．给出了多边形有理函数插值形函数的计算表达式．该插值格式以多边形的顶点作为插值点,插值形函数为有理函数形式,克服了传统有限方法中构造边数大于4单元多项式形式位移插值的困难．     

划线法构建Serendipity单元插值函数的几点思考

插值函数的构建在有限元分析中起着至关重要的作用,本文从一个变节点四边形等参单元的插值函数的构建出发,分析了划线法构建Serendipity单元插值函数时应注意的几点问题,提出了划线法构建插值函数时选择直线或曲线的原则,并通过3个例子验证了该结论.     

多边形有限单元形函数的比较研究

多边形有限单元形函数有wachspress插值、Laplace插值和平均值插值三种类型.本文对三种多边形有限单元形函数的性质作了比较研究,给出了三种形函数各自的优点和局限性.Waclaspress和Laplace形函数是有理函数形式,而平均值形函数是无理函数形式.三种形函数均满足单位分解性、线性完备性,且在单元边界上呈线性.在三角形单元上,它们都等价于三角形面积坐标插值.在矩形单元上,Wachspress和Laplace形函数等价于双线性多项式插值形函数.Wachspress和平均值形函数适用于任意凸多边形单元,Laplace形函数更适用于圆内接多边形单元.Wachspress形函数不能推广到含有边节点的单元,平均值形函数可以直接推广到含有边节点的单元.数值试验,验证了本文理论分析的结论.     

C1问题无单元法导函数递推公式

针对无单元方法MLS插值函数，采用正交基函数的导函数进行了详细推演，给出适用于薄板弯曲(C^1)问题的无单元方法导函数递推计算公式．     

建立基于力的变截面梁单元质量矩阵的新方法

基于位移的有限梁单元中三次Hermite插值函数不能有效地描述变截面梁单元内部位移变化,只能通过加密网格增加单元数解决,会造成计算量增大。基于力的有限梁单元由于使用的力插值函数不受截面形状变化的影响,在处理变截面梁时有很大优势,可以得到精确的位移插值函数,利用较少的单元可以达到很高的精度,解决了基于位移的有限梁单元在处理变截面梁时的不足。本文得到了考虑剪切变形的位移插值函数和考虑转动惯量的一致质量矩阵。利用算例验证了本文理论的正确性和高效性。     

Delaunay多边形单元的有理函数插值格式

本文提出了基于Delaunay多边形化的多边形单元有理函数插值格式。给出了Delaunay多边形化的概念和Delaunay多边形单元有理函数插值形函数的计算表达式。与Delaunay三角化网格不同，Delaunay多边形化网格形成对区域的唯一剖分。Delaunay多边形单元有理函数插值是以Delaunay多边形的顶点作为插值点，构造的有理函数形式插值。Delaunay多边形单元有理函数插值克服了有限元方法中难以构造边数大于4单元多项式形式位移插值的困难。有理函数插值形函数在多边形单元的内部是无穷次光滑的，在多边形的边界上是线性的。在三角形单元和矩形单元上，有理函数插值分别等价于有限元的三角形面积坐标插值和四边形双线性插值。给出了Delaunay多边形有理函数插值在圆域温度分布插值近似中的两个算例。     

一种区间B样条小波平板壳单元及应用

基于二维张量积区间B样条小波,构造了一种件能良好的小波平板壳单元．在小波单元的构造过程中,用二维区间B样条小波尺度函数取代传统多项式插值,在所构造的区间B样条平面弹性单元和平面Mindlin板单元的基础上组合而成．区间B样条小波单元同时具有B样条函数数值逼近精度高和多种用于结构分析的基函数的特点．数值算例表明：与传统有限元和解析解相比,构造的小波平板壳单元具有求解精度高,单元数量和自由度少等优点．     

基于自然单元法的功能梯度中厚板自由振动分析

自然单元法是一种基于自然邻近插值的无网格数值方法．相对于移动最小二乘近似而言,自然邻近插值不涉及到复杂的矩阵求逆运算,也不需要任何人为的参数．基于一阶剪切变形板理论,利用自然单元法对功能梯度中厚板的自由振动进行了数值分析．功能梯度板材料属性沿厚度方向呈梯度连续变化．由于自然邻近插值函数具有Kronecker delta函数性质,可以直接施加本质边界条件．通过本文给出的方法,对不同梯度指数和不同边界条件的功能梯度中厚板的振动频率进行了计算．通过与文献结果的对比验证了自然单元法求解的有效性．     

基于位移插值的Voronoi单元有限元方法

Voronoi单元有限元法是模拟颗粒增强复合材料非常先进有效的数值方法之一.为了克服它在构造插值函数时的困难,本文通过有限覆盖技术,对Voronoi单元进行了改进,提出了基于位移插值的Voronoi单元有限元方法,该方法的优点是只要知道夹杂中心点位置和Voronoi单元节点坐标,经过三次数学覆盖,即可形成Voronoi单元的位移插值函数.该方法形函数构造简单,容易实施.最后给出了数值模拟算例,并与现有的方法进行了比较.     

车桥耦合振动分析的两种常用插值方法比较

利用模态综合法分析车辆与桥梁之间的相互作用时,合理地构造桥梁的插值振型函数可以大幅提高计算精度.其中,分段三次Hermite插值函数和三次样条插值函数较为常用.为研究二者的异同,以简支梁桥为例分别采用这两种插值函数构造结构梁单元模型的一维插值振型函数和板单元模型的二维插值振型函数.基于以上两类插值振型函数,分析单自由度簧上质量匀速过桥时,桥梁的跨中位移、跨中梁底正应力和轮-桥接触力时程响应.结果表明:无论是一维问题还是二维问题,由三次样条插值法构造的插值振型函数与结构的实际振型较为吻合,计算结果具有较高的收敛性和精度.而要达到相同的精度,分段三次Hermite插值法则须加密单元网格,但其误差仅存在于独立网格内,不会累积放大.     

A NEW QUADRILATERAL THIN PLATE ELEMENT BASED ON THE MEMBRANE-PLATE SIMILARITY THEORY

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A new kind of mixed elements for shells of revolution subjected to arbitrary loads

In this paper a generalized variational principle with two-field variables is derived from the Reissner principle of elasticity in the curvilinear coordinates of a revolution shell, based on which, a new kind of mixed elements with independent transverse rotations is formulated for revolution shells subjected to harmonic external loads. The resultant-stress interpolations are carefully selected so that the shear part of the element stiffness contains the Kirchhoff hypothesis for thin shells and element stiffness matrices have correct ranks. The elements are free from shear locking and spurious kinematic modes. Numerical examples show that the new elements have good generality and high accuracy for thin and moderately-thick revolution shells.     

一类新型受任意载荷的杂交旋转壳单元

本文从弹性力学Reissner变分原理出发推导旋转壳曲线坐标系下内分，位移的二类变量广义变分原理，依据这个原理推导一类旋转壳坐标系中具有独立横向转角的受谐和外载荷下的杂交旋转壳单元，内力模式的选用使刚度矩阵的剪切部份在薄壳情况下能反映Kirchhoff假设，并使单元刚度矩阵满秩，从而保证单元无剪切自锁和零能模式，数例证明这类单元对中厚和薄旋转壳具有良好的通用性和较高的精度。     

Modeling of multilayer thin bodies

In this work, we considered the new parametrization of a multilayer thin domain. In particular, in contrast to classic approaches, we used several base surfaces and an analytic method with the application of orthogonal polynomial systems. We gave the vector parametric equation of each layer and the system of vector parametric equations of a multilayer thin domain and introduced the geometric characteristics for the proposed parametrization. We also derived the expressions for the transfer components of the second-rank identity tensor and the relations connecting the various families of bases and presented some differential operators, the system of equations of motion, the heat flow equation, the constitutive relations of the theory of the micropolar elasticity, and the Fourier heat conduction law under this parametrization of the thin-body domain. Finally, we gave the classification and statements of boundary value problems in the theory of thin bodies.     

Thermographic validation of a novel,laminate body,analytical heat conduction model

The two-region fin model captures the heat spreading behaviour in multilayered composite bodies (i.e., laminates), heated only over a small part of their domains (finite heat source), where there is an inner layer that has a substantial capacity for heat conduction parallel to the heat exchange surface (convection cooling). This resulting heat conduction behaviour improves the overall heat transfer process when compared to heat conduction in homogeneous bodies. Long-term heat storage using supercooling salt hydrate phase change materials, stovetop cookware, and electronics cooling applications could all benefit from this kind of heat-spreading in laminates. Experiments using laminate films reclaimed from post-consumer Tetra Brik cartons were conducted with thin rectangular and circular heaters to confirm the laminate body, steady-state, heat conduction behaviour predicted by the two-region fin model. Medium to high accuracy experimental validation of the two-region fin model was achieved in Cartesian and cylindrical coordinates for forced external convection and natural convection, the latter for Cartesian only. These were conducted using constant heat flux finite heat source temperature profiles that were measured by infrared thermography. This validation is also deemed valid for constant temperature heat sources.     

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to a moving heat source. The English text was polished by Yunming Chen.     

A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media

An arbitrarily curved three-dimensional anisotropic thin interphase between two anisotropic solids is considered. The purpose of this study is to model this interphase as a surface between its two neighbouring media by means of appropriately devised interface conditions on it. The analysis is carried out in the setting of unsteady heat conduction and dynamic elasticity, and makes use of the simple idea of a Taylor expansion of the relevant fields in thin regions. It consists of a generalization of a previous study by Bövik [1994. On the modelling of thin interface layers in elastic and acoustic scattering problems. Q. J. Mech. Appl. Math. 47, 17-42] which was confined to the isotropic setting. The remarkable feature of the presently derived anisotropic interface model is that formally it has a more compact form than that of Bövik's isotropic version. This is achieved by a judicious choice of surface differential operators which have been used in the derivation, and makes possible to show that several previously known classical interface models are recovered as special cases of the one obtained in this study, once suitable assumptions are made on the magnitude of the conductivity and elasticity tensors of the interphase.     

薄壳问题的一种数值解法

本文直接从三维弹性力学微分方程出发,依据三维的Kelvin解,应用最小二乘法建立了三维虚边界元法解薄壳问题的一般方法。本方法的显著优点是：不论求解何种壳体问题,思想是不变的,均以三维的Kelvin解来建立方程,而勿需对不同几何形状的壳本采用不同的基本解。文中给出了数值算例,以作为本方法的应用。本文方法与边界元直接法相比,优点在于无需处理奇异积分,且系数阵是对称的;再者,本文方法思想简单,程序实现容易。     

非傅立叶导热的最新研究进展

对迄今为止有关非傅立叶导热的研究成果进行了全面的综述,其中包括作者在该领域的最新研究进展:空心球体介质双曲线非傅立叶导热模型的分析求解,室温条件下多孔材料内非傅立叶导热的实验结果及数值模拟,非傅立叶导热的“瞬时薄层”模型,非傅立叶导热和非费克质量传递的耦合分析,非傅立叶导热的分子动力学模拟等．文中还对下一步的研究工作进行了展望.      

On the nature of the relaxation time,the Maxwell–Cattaneo and Fourier law in the thermodynamics of a continuous medium,and the scale effects in thermal conductivity

We present the theory of space–time elasticity and demonstrate that it is the extended reversible thermodynamics and gives the coupled model of thermoelasticity and heat conductivity and involves traditional thermoelasticity. We formulate the generally covariant variational model’s dynamic thermoelasticity and heat conductivity in which the basic kinematic and static variables are unified tensor objects (subject, matter). Variation statement defines the whole set of the initial-boundary problems for the 4D vector governing equation (Euler equation), the spatial projections of which define motion equations and the time projection gives the heat conductivity equation. We show that space–time elasticity directly implies the Fourier and the Maxwell–Cattaneo laws of heat conduction. However, space–time elasticity is richer than classical thermoelasticity, and it advocates its own equations of motion for coupled thermoelasticity. Moreover, we establish that the Maxwell–Cattaneo law and Fourier law can be defined for the reversible processes as compatibility equations without introducing dissipation. We argue that the present framework of space–time elasticity should prove adequate to describe the thermoelastic phenomena at low temperatures for interpreting the results of molecular simulations of heat conduction in solids and for the optimal heat and stress management in the microelectronic components and the thermoelectric devices.