A general super element for a curved beam

Corrugated panels have gained considerable popularity in a range of engineering applications, particularly in morphing skin applications. The optimum design of these structures needs simple models of the corrugated panels that may be incorporated into multi-disciplinary system models. Considering the geometric and mechanical properties of the corrugated panel, a generic super element of a corrugated core unit cell with elastomeric coating for morphing structures is investigated in this paper. The super element captures the small deformation of a 2D thin curved beam with variable curvature and is based on an exact analytical equivalent model which avoids any homogenization assumption. The stiffness matrix of a general curved beam element for a corrugated unit cell with elastomeric coating is derived. Different geometries are investigated to verify the accuracy and efficiency of the presented super element. The super element uses the geometric and mechanical properties of the panel as variables that may be applied for further topology optimization studies. The parametric studies of different corrugation shapes demonstrate the suitability of the proposed super element for application in further detailed design investigations.     

The analysis of thin walled composite laminated helicopter rotor with hierarchical warping functions and finite element method

In the present paper, a series of hierarchical warping functions is developed to analyze the static and dynamic problems of thin walled composite laminated helicopter rotors composed of several layers with single closed cell. This method is the development and extension of the traditional constrained warping theory of thin walled metallic beams, which had been proved very successful since 1940s. The warping distribution along the perimeter of each layer is expanded into a series of successively corrective warping functions with the traditional warping function caused by free torsion or free bending as the first term, and is assumed to be piecewise linear along the thickness direction of layers. The governing equations are derived based upon the variational principle of minimum potential energy for static analysis and Rayleigh Quotient for free vibration analysis. Then the hierarchical finite element method is introduced to form a numerical algorithm. Both static and natural vibration problems of sample box beams are analyzed with the present method to show the main mechanical behavior of the thin walled composite laminated helicopter rotor. The project supported by the National Natural Science Foundation of China (19932030)     

A new high-precision stress finite element for analysis of shell structures

A new high-precision finite element for analysis of shell structures is presented. It is derived from a slightly generalized equilibrium principle. Accordingly both stresses and displacements are obtained as primary result of analysis. At the assembly level the element has 45 degrees of freedom, all of them generalized displacements. For the price of some additional computational effort on the elemental level of analysis the proposed element is believed to gain certain advantages over the recently developed high-precision displacement elements. Thin as well as thick shell structures of arbitrary shape and loading can be equally analyzed. Engineering accuracy is attained with only very few elements. A variety of numerical examples demonstrates the applicability of the new element to all kinds of situations occuring in practice. A review of the existing high-precision shell elements is also included.     

大跨板片空间结构的超级有限元分析

板片空间结构是一种新型的结构体系，它是以一系列小板为基本构件，通过适当组合形成的具有空间受力性能的结构形式。本文在对这类结构有限元分析的基础上，应用超级元分析的基本思想，对这类结构进行了分析，给出了这类结构超级元分析方法的基本公式。算例分析结果表明：与一般有限元法相比，超级元法大大节省了计算量，结点自由度下降了二个数量级，且分析结果和有限元法基本吻合，为这类大跨空间结构应用微机分析提供了一个新的方法。     

橡胶复合材料结构大变形有限元分析

建立了一个橡胶复合材料结构有限元分析模型。在该模型中 ,考虑了轮胎变形的几何非线性、轮胎与地面和轮胎与轮辋的大变形非线性接触、轮胎材料的非均匀性和物理非线性及橡胶基复合材料的各向异性。此外 ,本文还利用该模型研制的有限元分析软件对全钢丝子午胎的变形轮廓进行了详细的分析。     

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.The project supported by the National Natural Science Foundation of China (10172023)     

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress–strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.     

A new twelve DOF quadrilateral element for analysis of thick and thin plates

A simple quadrilateral 12 DOF plate bending element based on Reissner–Mindlin theory for analysis of thick and thin plates is presented in this paper. This element is constructed by the following procedure:

• 1.the variation functions of the rotation and shear strain along each side of the element are determined using Timoshenko's beam theory; and
• 2.the rotation, curvature and shear strain fields in the domain of the element are then determined using the technique of improved interpolation.

The proposed element, denoted by ARS-Q12, is robust and free of shear locking and, thus, it can be employed to analyze very thin plate. Numerical examples show that the proposed element is a high performance element for thick and thin plates.     

A new curved gradient deficient shell element of absolute nodal coordinate formulation for modeling thin shell structures

A curved gradient deficient shell element for the Absolute Nodal Coordinate Formulation (ANCF) is proposed for modeling initially thin curved structures. Unlike the fully parameterized elements of ANCF, a full mapping of the gradient vectors between different configurations is not available for gradient deficient elements, therefore it is cumbersome to work in a rectangular coordinate system for an initially curved element. In this study, a curvilinear coordinate system is adopted as the undeformed Lagrangian coordinates, and the Green–Lagrange strain tensor with respect to the curvilinear frame is utilized to characterize the deformation energy of the shell element. As a result, the strain due to the initially curved element shape is eliminated naturally, and the element formulation is obtained in a concise mathematical form with a clear physical interpretation. For thin structures, the simplified formulations for the evaluation of elastic forces are also given. Moreover, an approach to deal with the on-surface slope discontinuity is also proposed for modeling general curved shell structures. Finally, the developed element of ANCF is validated by several numerical examples.     

A thin-walled composite beam model for light-weighted structures interacting with fluids

A thin-walled beam model is proposed for structures of variable cross-section, which can be either open or closed and includes multicellular cross-sections with either isotropic or orthotropic materials. The proposed model does not require any priori definition of cross-sectional warping which instead results from the solution of the problem. To achieve that a special deformation pattern is superimposed on the bending deformation described by Euler–Bernoulli beam theory. All sectional properties are automatically incorporated in the analysis as a result of the usual variational formulation of the system of equations. The proposed model is specifically designed to simulate the dynamics of wind/hydrokinetic turbine blade with low computational cost, especially in fluid–structure interaction (FSI) simulation. A number of test cases have been carried out to validate the proposed structural model which show good agreement between the results obtained her e and the solutions available in literature. Finally, FSI simulation of a hydrokinetic blade under field condition is carried out to illustrate the capability of the current thin-walled beam model in practice.     

Three-dimensional large deformation analysis of thin walled beams

A set of kinematic assumptions and constraints is used to develop a formulation for the analysis of thin-walled beams, of arbitrary open cross-section, subjected to arbitrarily large displacements in three-dimensional space. The validity of the formulation is illustrated through numerical solutions for elastic lateral-torsional post-buckling behavior of “I” beams, and a comparison of these solutions with experimental results.     

Stochastic boundary element method for reliability analysis of plate and beams composite structures

I.IntroductionTheengineeringstructuresareoftells,'1>:'rectcdtotheactionofthestochasticloadingthatvarieswiththetime,forexample,theengineeringstructuresactedonbytheearthquake,theoceanstructuresactedonbydynamicpressure,andthevehiclesofthetransportationinflue…     

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 catenary element for the analysis of cable structures

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一种薄壳厚壳通用的轴对称曲壳单元

有限元法分析轴对称壳体时，常需区分薄壳和厚壳并选用不同的单元，给计算带来不便．为此，通过对现有的轴对称壳体单元的研究，基于加权残值法，将广义协调条件引入剪应变场，构造了一种挠度和转角各自独立的新型轴对称曲壳单元．算例结果表明，新单元具有很高的精度，既可用于厚壳，也可用于薄壳．该单元可用于轴对称壳体结构的计算分析．     

Elastodynamic analysis of low tension cables using a new curved beam element

In this paper, we address and overcome the difficulties associated with the use of the classic cable theory to treat low tension cables by developing a new three-noded locking-free nonlinear curved beam element. Based upon nonlinear generalized curved beam theory, large deformations and rotations in the new element are formulated in terms of Updated Lagrangian framework. Consistently coupled polynomial displacement fields are used to satisfy the membrane locking-free condition and the requirement of being able to recover the inextensible bending modes. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results are presented to demonstrate the superior accuracy and the high convergence rate of the newly developed curved beam element. The stability and accuracy of the new element are further validated by experiments of an instrumented free-swinging steel cable experiencing slack and low tension. Good agreements in cable position and tension are observed between the experimental results and the finite element predictions.     

Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity

This work presents a new multi-layer laminated composite structure model to predict the mechanical behaviour of multi-layered laminated composite structures. As a case study, the mechanical behaviour of laminated composite beam (90°/0°/0°/90°) is examined from both a static and dynamic point of view. The results are compared with the model “Sinus” and finite element method studied by Abou Harb. Results show that this new model is more precise than older ones as compared to the results by the finite element method (Abaqus). To introduce continuity on the interfaces of each layer, the kinematics defined by Ossadzow was used. The equilibrium equations and natural boundary conditions are derived by the principle of virtual power. To validate the new proposed model, different cases in bending, buckling and free vibration have been considered.     

张拉结构非线性分析的五节点等参单元

本文针对张拉结构的特点，提出了一种五节点等参数单元有限元模型，采用四次多项式作为位移插值函数及单元初始形状函数，并假定索是理想柔性的且满足虎克定律，基于修正的Ｌａｇｒａｎｇｉａｎ坐标描述法，建立了非线性有限元基本方程和切线刚度矩阵，利用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法进行了实例计算。结果表明：本文方法精度极高，可供大跨度索网，索穹顶，拉线塔等张拉结构分析，设计时采用。