A nonlinear quadrilateral shell element with drilling degrees of freedom

Summary A bending theory for thin shells undergoing finite deformations is presented, and its associated finite element model is described. The kinematic assumptions are of Reissner-Mindlin type. The formulation is based on the introduction of a mixed functional with independent in-plane rotation field and skew-symmetric part of membrane forces. The resulting Euler-Lagrangian equations yield the equilibrium of stress resultants and the couple resultant with respect to the surface normal. Furthermore, the equality of the independent rotation field with the displacement dependent rotation field is enforced. Hence, the symmetry of the stress resultants is fulfilled in a weak sence. Naturally, the development of a quadrilateral finite element includes drilling degrees of freedom. The displacement field is approximated using an Allman-type interpolation.

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Ein nichtlineares Vier-Knoten-Schalenelement unter Verwendung von Drehfreiheitsgraden in der Schalenmittelfläche

Übersicht Es wird eine Biegetheorie dünner Schalen bei finiten Deformationen sowie die zugehörige Finite-Element-Formulierung vorgestellt. Die kinematischen Annahmen sind vom Reissner-Mindlin-Typ. Die Darstellung basiert auf der Einführung eines gemischten Funktionals mit unabhängigen Drehfreiheitsgraden in der Schalenmmittelfläche und einem schiefsymmetrischen Anteil der Membrankräfte. Die resultierenden Euler-Lagrange-Gleichungen ergeben das Gleichgewicht und die Symmetrie der Schnittgrößen. Weiterhin ergibt sich die Gleichheit des unabhängigen mit dem verschiebungsabhängigen Rotationsfeld. Die Entwicklung des Vier-Knoten-Schalenelementes enthält somit auch den Drehfreiheitsgrad um die Schalenormale. Für das Verschiebungsfeld wird ein Allman-Ansatz gewählt.

     

带旋转自由度C^0类任意四边形板（壳）单元

基于Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｉｌｉｎ板弯曲理论和Ｖｏｎ－Ｋａｒｍａｎ大挠度理论,采用单元域内和边界位移插值一致性的概念,将四节点等参弯曲单元与Ａｌｌｍａｎ膜变形二次插值模式相结合,对层合板壳的大挠度分析提供了一种实用的带旋转自由度的四节点Ｃ＾０类板单元。大量算例表明：该单元对板壳结构的线性强度、稳定性和后屈曲分析都表现出良好的收敛性和足够的工程精度。     

A novel four-node quadrilateral element with continuous nodal stress

Formulation and numerical evaluation of a novel four-node quadrilateral element with continuous nodal stress（Q4-CNS）are presented.Q4-CNS can be regarded as an improved hybrid FE-meshless four-node quadrilateral element（FE-LSPIM QUAD4）, which is a hybrid FE-meshless method.Derivatives of Q4-CNS are continuous at nodes, so the continuous nodal stress can be obtained without any smoothing operation.It is found that,compared with the standard four-node quadrilateral element（QUAD4）,Q4- CNS can achieve significantly better accuracy and higher convergence rate.It is also found that Q4-CNS exhibits high tolerance to mesh distortion.Moreover,since derivatives of Q4-CNS shape functions are continuous at nodes,Q4-CNS is potentially useful for the problem of bending plate and shell models.     

Incompatible curved quadrilateral plate bending element with 12-degrees of freedom

This paper presents a new curved quadrilateral plate element with12-degree freedom by the exact element method.The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle.Using this method,the compatibility conditions between element can be treated very easily,if displacements and stress resultants are continuous at nodes between elements.The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed.Numerical examples are given at the end of this paper,which show the excellent precision and efficiency of the new element.     

A NEW HYBRID QUADRILATERAL FINITE ELEMENT FOR MINDLIN PLATE

ＡＮＥＷＨＹＢＲＩＤＱＵＡＤＲＩＬＡＴＥＲＡＬＦＩＮＩＴＥＥＬＥＭＥＮＴＦＯＲＭＩＮＤＬＩＮＰＬＡＴＥＣｈｉｎＹｉ（秦奕）（ＴｉａｎｊｉｎＡｒｃｈｉｔｅｃｔｕｒａｌＤｅｓｉｇｎＩｎｓｔｉｔｕｔｅ，Ｔｉａｎｊｉｎ）ＺｈａｎｇＪｉｎｇ－ｙｕ（张敬宇）（Ｉ...     

An hysteretic quadrilateral plane stress element

In this work, a new plane stress element is proposed for the nonlinear static and dynamic analysis of plane stress/plane strain problems. The four node quadrilateral element formulation for the elastic case is extended by introducing a novel hysteretic constitutive relation, based on the Bouc–Wen model of hysteresis. The hysteretic model introduced is directly derived from the governing equations of classical plasticity based on the flow rule and specific hardening law. The stiffness matrix of the element is formulated using the principle of virtual displacements, where the elastic stress–strain relation is substituted by the hysteretic relation proposed. The derived stiffness matrix is expressed as a smooth function of the internal stress field both in the elastic and inelastic regime. The efficiency of the proposed element in the simulation of the cyclic behavior in plane structures is presented through illustrative examples.     

A cubic quadrilateral spline element with concave shapes

Basic requirement for applying isoparametric element is that the element has to be convex and no violent distortion is allowed. In this paper, a cubic quadrilateral spline element with 12 nodes has been developed using the triangular area coordinates and the B-net method, which can exactly model the cubic field for quadrilateral element with both convex and concave shapes. Neither mapping nor coordinate transformation is required and the spline element can obtain high accuracy solutions and insensitive to mesh distortions.     

A penalty-equilibrating hybrid stress 3-D element

This paper presents a theory about penalty-equilibrating(PEQ) hybrid element of three dimensions (3-D), and generates a model for the PEQ hybrid stress 3-D element. By the PEQ approach, the false stress is avoided and the precision in calculation is raised to a large extent under the mesh distortion condition without another additional degree of freedom. In the results of numerical examples, the present element is compared with the 8-node hexahedron element and the optimized hybrid element, and it is proved that our conclusion is correct. In addition, the penalty-equilibrating hybrid 3-D element is taken as a trial to calculate problems of square plate bending and incompressibility. The results obtained are satisfactory.     

The explicit forms of field functions in totrahedron element with 16 and 20 degrees of freedom

In this paper, the explicit forms of field functions in tetrehedron elements with 16 and 20 degrees of freedom are given in terms of volume coordinatesL ₁,L ₂,L ₃,L ₄ of tetrahedron.     

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.     

一个不闭锁和抗畸变的四边形厚板元

构造一个彻底消除剪切闭锁现象并且对网格畸变不敏感的四边形厚薄板通用单元RPAQ。在方法上有三个特点：第一,在厚板挠度和转角的试函数中,采用了合理匹配方案,从而在源头上彻底消除了剪切闭锁现象;第二,采用四边形面积坐标,以代替通常的等参坐标,从而使网格畸变时仍然保持高精度;第三,采用广义协调元做法,使协调条件的采用灵活多样,并保证单元的收敛性。进行了一系列数值例题测试,表明单元RPAQ能自动消除闭锁现象,在由薄板到厚板的不同情况下,在各种网格畸变的情况下,都能体现出良好的精度和数值稳定性。     

A study of the hybrid element methods for stress analysis

A new functional which forms the basis of an improved hybrid element formulation is proposed. The variables for the functional include stresses, strains and displacements, and the displacements and stresses are further decomposed into two parts respectively. The proposed new formulation appears to be particularly suitable for improving conforming models.The relationship between the new hybrid elements and the conventional displacement elements are also explored in this paper.     

A modified airfoil-based piezoaeroelastic energy harvester with double plunge degrees of freedom

In this letter,a piezoaeroelastic energy harvester based on an airfoil with double plunge degrees of freedom is proposed to additionally take advantage of the vibrational energy of the airfoil pitch motion.An analytical model of the proposed energy harvesting system is built and compared with an equivalent model using the well-explored pitch-plunge configuration.The dynamic response and average power output of the harvester are numerically studied as the flow velocity exceeds the cut-in speed(flutter speed).It is found that the harvester with double-plunge configuration generates 4%–10% more power with varying flow velocities while reducing 6% of the cut-in speed than its counterpart.     

A model kinetic equation for a gas with rotational degrees of freedom

A model kinetic equation for a gas with rotational degrees of freedom is obtained. By averaging of the distribution function over quantities corresponding to the rotational degrees of freedom this equation is reduced to a closed system of two kinetic equations, each of which is analogous to the kinetic equation of a monatomic gas.     

On the equivalence of non-conforming element and hybrid stress element

This paper is intended to show that the non-conforming element by Wilson[³] et al. and the hybrid stress element by Pian[²] are equivalent.     

A URI 4-Node quadrilateral element by assumed strain

In this paper one-point quadrature ““““assumed strain““““ mixed element formulation based on the Hu-Washizu variational principle is presented. Special care is taken to avoid hourglass modes and volumetric locking as well as shear locking. The assumed strain fields are constructed so that those portions of the fields which lead to volumetric and shear locking phenomena are eliminated by projection, while the implementation of the proposed URI scheme is straightforward to suppress hourglass modes. In order to treat geometric nonlinearities simply and efficiently, a corotational coordinate system is used. Several numerical examples are given to demonstrate the performance of the suggested formulation, including nonlinear static/dynamic mechanical problems.     

Model optimization of hybrid stress general shell element

A 20 DOF (degree of freedom) hybrid stress element based upon Mindlin plate bending theory is developed using the optimizing design method for thin and moderately thick shell. It is of quadrilateral shape with only four corner nodes and can be used for both shallow and deep shells with excellent performance and the shear locking problem no longer exists.The project supported by National Science Foundation of China.