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X. G. Tan L. Vu‐Quoc 《International journal for numerical methods in engineering》2005,63(15):2124-2170
We present in this paper an efficient and accurate low‐order solid‐shell element formulation for analyses of large deformable multilayer shell structures with non‐linear materials. The element has only displacement degrees of freedom (dofs), and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out‐of‐plane bending) and to remedy volumetric locking. Based on the mixed Fraeijs de Veubeke‐Hu‐Washizu (FHW) variational principle, the in‐plane and out‐of‐plane bending behaviours are improved and the locking associated with (nearly) incompressible materials is avoided via a new efficient enhancement of strain tensor. Shear locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. Two non‐linear 3‐D constitutive models (Mooney–Rivlin material and hyperelastoplastic material at finite strain) are applied directly without requiring the enforcement of the plane‐stress assumption. In particular, we give a simple derivation for the hyperelastoplastic model using spectral representations. In addition, the present element has a well‐defined lumped mass matrix, and provides double‐side contact surfaces for shell contact problems. With the dynamics referred to a fixed inertial frame, the present element can be used to analyse multilayer shell structures undergoing large overall motion. Numerical examples involving static analyses and implicit/explicit dynamic analyses of multilayer shell structures with both material and geometric non‐linearities are presented, and compared with existing results obtained from other shell elements and from a meshless method. It is shown that elements that did not pass the out‐of‐plane bending patch test could not provide accurate results, as compared to the present element formulation, which passed the out‐of‐plane bending patch test. The present element proves to be versatile and efficient in the modelling and analyses of general non‐linear composite multilayer shell structures. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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Lin Quan Yao Li Lu 《International journal for numerical methods in engineering》2003,58(10):1499-1522
Eighteen‐node solid‐shell finite element models have been developed for the analysis of laminated composite plate/shell structures embedded with piezoelectric actuators and sensors. The explicit hybrid stabilization method is employed to formulate stabilization vectors for the uniformly reduced integrated 18‐node three‐dimensional composite solid element. Unlike conventional piezoelectric elements, the concept of the electric nodes introduced in this paper can effectively eliminate the burden of constraining the equality of the electric potential for the nodes lying on the same electrode. Furthermore, the non‐linear distribution of electric potential in the piezoelectric layer is expressed by introducing internal electric potential, which not only can simplify modelling but also obtains the same as the exact solution. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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K. Y. Sze S. H. Lo L.‐Q. Yao 《International journal for numerical methods in engineering》2002,53(12):2617-2642
In this paper, we start with a modified generalized laminate stiffness matrix that serves as a remedy to resolve the thickness locking and some abnormalities encountered by solid‐shell elements in laminate analyses. A modified Hellinger–Reissner functional having displacement and a set of generalized stresses as independent fields is devised. Based upon the functional, eight‐node and 18‐node hybrid‐stress solid‐shell elements are proposed. A number of benchmark tests on homogenous and laminated plates/shells are conducted. The accuracy of the elements is promising. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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Christian Miehe Nikolas Apel 《International journal for numerical methods in engineering》2004,61(12):2067-2113
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Y. Y. Lee H. Y. Sun J. N. Reddy 《International journal for numerical methods in engineering》2006,65(1):45-61
A theoretical analysis is presented for the large amplitude vibration of symmetric and unsymmetric composite plates using the non‐linear finite element modal reduction method. The problem is first reduced to a set of Duffing‐type modal equations using the finite element modal reduction method. The main advantage of the proposed approach is that no updating of the non‐linear stiffness matrices is needed. Without loss of generality, accurate frequency ratios for the fundamental mode and the higher modes of a composite plate at various values of maximum deflection are then determined by using the Runge–Kutta numerical integration scheme. The procedure for obtaining proper initial conditions for the periodic plate motions is very time consuming. Thus, an alternative scheme (the harmonic balance method) is adopted and assessed, as it was employed to formulate the large amplitude free vibration of beams in a previous study, and the results agreed well with the elliptic solution. The numerical results that are obtained with the harmonic balance method agree reasonably well with those obtained with the Runge–Kutta method. The contribution of each linear mode to the maximum deflection of a plate can also be obtained. The frequency ratios for isotropic and composite plates at various maximum deflections are presented, and convergence of frequencies with the number of finite elements, number of linear modes, and number of harmonic terms is also studied. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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G. M. Kulikov S. V. Plotnikova 《International journal for numerical methods in engineering》2011,88(13):1363-1389
This paper presents the finite rotation exact geometry (EG) 12‐node solid‐shell element with 36 displacement degrees of freedom. The term ‘EG’ reflects the fact that coefficients of the first and second fundamental forms of the reference surface and Christoffel symbols are taken exactly at each element node. The finite element formulation developed is based on the 9‐parameter shell model by employing a new concept of sampling surfaces (S‐surfaces) inside the shell body. We introduce three S‐surfaces, namely, bottom, middle and top, and choose nine displacements of these surfaces as fundamental shell unknowns. Such choice allows one to represent the finite rotation higher order EG solid‐shell element formulation in a very compact form and to derive the strain–displacement relationships, which are objective, that is, invariant under arbitrarily large rigid‐body shell motions in convected curvilinear coordinates. The tangent stiffness matrix is evaluated by using 3D analytical integration and the explicit presentation of this matrix is given. The latter is unusual for the non‐linear EG shell element formulation. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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采用子结构法研究了重载列车引起的大跨度铁路斜拉桥拉索非线性振动问题。首先基于线性桥梁空间有限元模型,采用车-桥耦合动力学理论计算得到斜拉索锚固点动力响应;然后将该动力响应作为斜拉索端部激励,采用自编的基于CR列式法(Co-rotational Formulation)的拉索非线性动力有限元程序,计算斜拉索非线性动力响应。以荆岳铁路洞庭湖三塔斜拉桥为例,开展了车致斜拉桥拉索振动分析,结果表明:在设计时速范围内,重载列车作用下,斜拉桥索端激励与拉索固有频率两者不存在明显的匹配关系,车致拉索振动响应为一个准静态过程;通过进一步对比不同计算方案,即车-桥耦合振动、移动轴重瞬态分析与移动轴重影响线加载对拉索响应的影响,发现对于大跨度铁路斜拉桥而言,由于车-桥耦合振动效应不显著,采用移动轴重影响线加载方法得到的拉索应力结果具有足够精度。 相似文献
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X. Q. He K. M. Liew T. Y. Ng S. Sivashanker 《International journal for numerical methods in engineering》2002,54(6):853-870
In this paper, a generic finite element formulation is developed for the static and dynamic control of FGM (functionally graded material) shells with piezoelectric sensor and actuator layers. The properties of the FGM shell are graded in the thickness direction according to a volume fraction power‐law distribution. The proposed finite element model is based on variational principle and linear piezoelectricity theory. A constant displacement and velocity feedback control algorithm coupling the direct and inverse piezoelectric effects is applied in a closed‐loop system to provide feedback control of the integrated FGM shell structure. Both static and dynamic control of FGM shells are simulated to demonstrate the effectiveness of the proposed active control scheme within a framework of finite element discretization and piezoelectric integration. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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K. Rah W. Van Paepegem A. M. Habraken J. Degrieck 《International journal for numerical methods in engineering》2012,89(7):805-828
This paper presents a versatile low order locking‐free mixed solid‐shell element that can be readily employed for a wide range of linear elastic structural analyses, that is, from thick isotropic structures to multilayer anisotropic composites. This solid‐shell element has eight nodes with only displacement degrees of freedom and few assumed stress parameters that provide very accurate interlaminar stress calculations through the element thickness. These elements can be stacked on top of each other to model multilayer structures, fulfilling the interlaminar stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of the laminate. The element formulation is based on the well‐known Fraeijs de Veubeke–Hu–Washizu mixed variational principle with enhanced assumed strains formulation and assumed natural strains formulation to alleviate the different types of locking phenomena in solid‐shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar stress field in multilayer structures, which is achieved by the introduction of a constraint equation on the interlaminar stresses in the Fraeijs de Veubeke–Hu–Washizu principle‐based enhanced assumed strains formulation. The intelligent computer coding of the present formulation makes the present element appropriate for a wide range of structural analyses. To assess the present formulation's accuracy, a variety of popular numerical benchmark examples related to element convergence, mesh distortion, and shell and laminated composite analyses are investigated and the results are compared with those available in the literature. These benchmark examples reveal that the proposed formulation provides very good results for the structural analysis of shells and multilayer composites. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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针对有限元逆分析方法进行荷载识别的大计算量的缺陷,以及鉴于传统的BP网络的速度慢和局部极小值问题,该文提出了将有限元方法与径向基函数(Radial Base Function,简记为RBF)神经网络结合对受集中载荷作用的壳体结构进行荷载识别。通过有限元方法计算出压电元件的集聚电荷,以该电荷来构建训练样本对网络进行训练,再将没有进行训练的电荷数据送入到训练好的RBF神经网络进行预测,实现对壳体结构荷载的作用位置和大小的评估。最后给出了对壳体结构荷载识别的算例,结果表明该方法计算速度快、精度高、具有较好的应用前景。 相似文献
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基于一阶剪切效应Mindlin板理论,建立了在热载下含分布式压电作动器的复合材料层合板有限元分析模型和控制方程,分别研究了该板在内外表面存在温差的情况下的热变形,以及使用压电作动器对热变形区域进行形状修复的问题;在分析中考虑了压电作动器与复合材料层合板间含有胶接层的影响。由典型算例结果讨论,得到如下结论:1)使用压电作动器可以有效地对复合材料层合板的表面热变形形状进行修复;2)压电作动器的分布位置对修复效果影响很大;3)在电压达到一定数值后,继续增加电压值对修复效果贡献很小。 相似文献
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K. Rah W. Van Paepegem J. Degrieck 《International journal for numerical methods in engineering》2013,93(2):201-223
In the present contribution we propose an optimal low‐order versatile partial hybrid stress solid‐shell element that can be readily employed for a wide range of geometrically linear elastic structural analyses, that is, from shell‐like isotropic structures to multilayer anisotropic composites. This solid‐shell element has eight nodes with only displacement degrees of freedom and only a few internal parameters that provide the locking‐free behavior and accurate interlaminar shear stress resolution through the element thickness. These elements can be stacked on top of each other to model multilayer composite structures, fulfilling the interlaminar shear stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of composite laminates. The element formulation is based on the modified form of the well‐known Fraeijs de Veubeke–Hu–Washizu multifield variational principle with enhanced assumed strains formulation and assumed natural strains formulation to alleviate the different types of locking phenomena in solid‐shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar shear stress field in multilayer structures, which is achieved by the introduction of the assumed interlaminar shear stress field in a standard enhanced assumed strains formulation based on the Fraeijs de Veubeke–Hu–Washizu principle. The numerical testing of the present formulation, employing a variety of popular numerical benchmark examples related to element patch test, convergence, mesh distortion, shell and laminated composite analyses, proves its accuracy for a wide range of structural analyses.Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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E. Verron G. Marckmann B. Peseux 《International journal for numerical methods in engineering》2001,50(5):1233-1251
The present paper deals with the dynamic inflation of rubber‐like membranes.The material is assumed to obey the hyperelastic Mooney's model or the non‐linear viscoelastic Christensen's model. The governing equations of free inflation are solved by a total Lagrangian finite element method for the spatial discretization and an explicit finite‐difference algorithm for the time‐integration scheme. The numerical implementation of constitutive equations is highlighted and the special case of integral viscoelastic models is examined in detail. The external force consists in a gas flow rate, which is more realistic than a pressure time history. Then, an original method is used to calculate the pressure evolution inside the bubble depending on the deformation state. Our numerical procedure is illustrated through different examples and compared with both analytical and experimental results. These comparisons yield good agreement and show the ability of our approach to simulate both stable and unstable large strain inflations of rubber‐like membranes. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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运用振动反分析方法计算振动荷载 总被引：7，自引：0，他引：7
本文研究运用振动反问题理论求解振动荷载时程的问题。在Newmark法求解运动平衡方程的基础上,推导了求解振动荷载的公式。采用最小二乘法估计最可置信的荷载系数。提出了由结构对振动荷载的反应求振动荷载时程的有限元方法。通过算例验证了方法的有效性。本文为计算振动荷载提供了一种新的方法。 相似文献