共查询到20条相似文献，搜索用时 15 毫秒
1.
K. Schulz S. Klinkel W. Wagner 《International journal for numerical methods in engineering》2011,87(6):491-520
In this paper, we present a non‐linear finite element formulation for piezoelectric shell structures. Based on a mixed multi‐field variational formulation, an electro‐mechanical coupled shell element is developed considering geometrically and materially non‐linear behavior of ferroelectric ceramics. The mixed formulation includes the independent fields of displacements, electric potential, strains, electric field, stresses, and dielectric displacements. Besides the mechanical degrees of freedom, the shell counts only one electrical degree of freedom. This is the difference in the electric potential in the thickness direction of the shell. Incorporating non‐linear kinematic assumptions, structures with large deformations and stability problems can be analyzed. According to a Reissner–Mindlin theory, the shell element accounts for constant transversal shear strains. The formulation incorporates a three‐dimensional transversal isotropic material law, thus the kinematic in the thickness direction of the shell is considered. The normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and the resultant dielectric displacement fields. Accounting for material non‐linearities, the ferroelectric hysteresis phenomena are considered using the Preisach model. As a special aspect, the formulation includes temperature‐dependent effects and thus the change of the piezoelectric material parameters due to the temperature. This enables the element to describe temperature‐dependent hysteresis curves. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
2.
C. S. Long P. W. Loveday Albert A. Groenwold 《International journal for numerical methods in engineering》2006,65(11):1802-1830
Several new planar four node piezoelectric elements with drilling degrees of freedom are presented. We begin by deriving two families of variational formulations accounting for piezoelectricity and in‐plane rotations. The first family retains the skew‐symmetric part of the stress tensor, while in the second, the skew part of stress is eliminated from the functional. The finite elements derived from two of the variational formulations derived in this paper are investigated. The first element is based on an ‘irreducible’ form, while the other is based on a fully mixed functional, with both stress and electric flux density assumed. Our new elements are shown to be accurate and robust in comparison with a number of existing elements, for several benchmark test problems. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
3.
A simple triangular solid shell element formulation is developed for efficient analysis of plates and shells undergoing finite rotations. The kinematics of the present solid shell element formulation is purely vectorial with only three translational degrees of freedom per node. Accordingly, the kinematics of deformation is free of the limitation of small angle increments, and thus the formulation allows large load increments in the analysis of finite rotation. An assumed strain field is carefully selected to alleviate the locking effect without triggering undesirable spurious kinematic modes. In addition, the curved surface of shell structures is modeled with flat facet elements to obviate the membrane locking effect. Various numerical examples demonstrate the efficiency and accuracy of the present element formulation for the analysis of plates and shells undergoing finite rotation. The present formulation is attractive in that only three points are needed for numerical integration over an element. 相似文献
4.
E. Carrera M. Boscolo 《International journal for numerical methods in engineering》2007,70(10):1135-1181
5.
Y. Y. KIM J. G. KIM 《International journal for numerical methods in engineering》1996,39(11):1903-1914
An efficient, perhaps simplest, three-noded mixed finite element is proposed for axisymmetric shell analysis. The key feature in the present formulation is to start with a better variational principle in which the independent unknowns are only the quantities that can be prescribed at the shell edges. If the consistency for field approximations is satisfied, no other numerical consideration is necessary in the present element. Several examples confirm the satisfactory numerical behaviour of the present mixed element. 相似文献
6.
This paper is concerned with the development of new simple 4-noded locking-alleviated smart finite elements for modeling the smart composite beams. The exact solutions for the static responses of the overall smart composite beams are also derived for authenticating the new smart finite elements. The overall smart composite beam is composed of a laminated substrate conventional composite beam, and a piezoelectric layer attached at the top surface of the substrate beam. The piezoelectric layer acts as the actuator layer of the smart beam. Alternate finite element models of the beams, based on an “equivalent single layer high order shear deformation theory”, and a “layer-wise high order shear deformation theory”, are also derived for the purpose of investigating the required number of elements across the thickness of the overall smart composite beams. Several cross-ply substrate beams are considered for presenting the results. The responses computed by the present new “smart finite element model” excellently match with those obtained by the exact solutions. The new smart finite elements developed here reveal that the development of finite element models of smart composite beams does not require the use of conventional first order or high order or layer-wise shear deformation theories of beams. Instead, the use of the presently developed locking-free 4-node elements based on conventional linear piezo-elasticity is sufficient. 相似文献
7.
Stefanos-Aldo Papanicolopulos Fahad Gulib Aikaterini Marinelli 《International journal for numerical methods in engineering》2019,117(8):926-937
Various finite elements based on mixed formulations have been proposed for the solution of boundary value problems involving strain-gradient models. The relevant literature, however, does not provide details on some important theoretical aspects of these elements. In this work, we first present the existing elements within a novel, single mathematical framework, identifying some theoretical issues common to all of them that affect their robustness and numerical efficiency. We then proceed to develop a new family of mixed elements that addresses these issues while being simpler and computationally cheaper. The behavior of the new elements is further demonstrated through two numerical examples. 相似文献
8.
F. Auricchio P. Bisegna C. Lovadina 《International journal for numerical methods in engineering》2001,50(6):1469-1499
A Reissner–Mindlin‐type modellization of piezoelectric plates is here considered in a suitable variational framework. Both the membranal and the bending behaviour are studied as the thickness of the structure tends to zero. A finite element scheme able to approximate the solution is then proposed and theoretically analysed. Some numerical results showing the performances of the scheme under consideration are discussed. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
9.
Philippe Remy Bernard Devloo Omar Durán Agnaldo Monteiro Farias Sônia Maria Gomes 《International journal for numerical methods in engineering》2020,121(13):2896-2915
Effects of nonaffine elements on the accuracy of 3D H(div)-conforming finite elements are studied. Instead of convergence order k+1 for the flux and the divergence of the flux obtained with Raviart-Thomas or Nédélec spaces with normal traces of degree k, based on affine hexahedra or triangular prisms, reduced orders k for the flux and k−1 for the divergence of the flux may occur for distorted elements. To improve this scenario, a hierarchy of enriched flux approximations is considered, by adding internal shape functions up to a higher degree k+n, n>0, while keeping the original normal traces of degree k. The resulting enriched approximations, using multilinear transformations, keep the original flux accuracy (of order k+1 with affine elements or reduced order k otherwise), but enhanced divergence (of order k+n+1, in the affine case, or k+n−1 otherwise) can be reached. The reduced flux accuracy due to quadrilateral face distortions cannot be corrected by including higher order internal functions. The enriched spaces are applied to the mixed finite element formulation of Darcy's model. The computational cost of matrix assembly increases with n, but the condensed system to be solved has the same dimension and structure as the original scheme. 相似文献
10.
11.
In the recent years, solid‐shell finite element models which possess no rotational degrees of freedom and applicable to thin plate/shell analyses have attracted considerable attention. Development of these elements are not straightforward. Shear, membrane, trapezoidal, thickness and dilatational lockings must been visioned. In this part of this paper, a novel eight‐node solid‐shell element is proposed. To resolve the shear and trapezoidal lockings, the assumed natural strain (ANS) method is resorted to. The hybrid‐stress formulation is employed to rectify the thickness and dilatational locking. The element is computationally more efficient than the conventional hybrid elements by adopting orthogonal‐assumed stress modes and enforcing admissible sparsity in the flexibility matrix. Popular benchmark tests are exercised to illustrate the efficacy of the elements. In Part II of the paper, the element will be generalized for smart structure modelling by including the piezoelectric effect. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
12.
Won I. Hong Yong H. Kim Sung W. Lee 《International journal for numerical methods in engineering》2001,52(4):455-469
Bubble function displacements are used in conjunction with the assumed strain formulation to construct efficient triangular solid shell elements tailored for shell analysis. Two versions of 36‐DOF triangular elements are presented with different bubble function displacements and the corresponding assumed strain fields. In the first version the bubble function displacement is independent of the thickness while in the second version the bubble function varies linearly in the thickness direction. The assumed strain fields are carefully selected to alleviate locking effect. The first version models curved shells with flat triangular elements. The second version is effective in alleviating the membrane locking and thus allows more accurate modelling of curved shells. Various numerical examples demonstrate the validity and effectiveness of the present assumed strain formulation elements with the bubble function displacements. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
13.
Srivathsan Ravi Andreas Zilian 《International journal for numerical methods in engineering》2017,112(12):1828-1847
The successful design of piezoelectric energy harvesting devices relies upon the identification of optimal geometrical and material configurations to maximize the power output for a specific band of excitation frequencies. Extendable predictive models and associated approximate solution methods are essential for analysis of a wide variety of future advanced energy harvesting devices involving more complex geometries and material distributions. Based on a holistic continuum mechanics modeling approach to the multi‐physics energy harvesting problem, this article proposes a monolithic numerical solution scheme using a mixed‐hybrid 3‐dimensional finite element formulation of the coupled governing equations for analysis in time and frequency domain. The weak form of the electromechanical/circuit system uses velocities and potential rate within the piezoelectric structure, free boundary charge on the electrodes, and potential at the level of the generic electric circuit as global degrees of freedom. The approximation of stress and dielectric displacement follows the work by Pian, Sze, and Pan. Results obtained with the proposed model are compared with analytical results for the reduced‐order model of a cantilevered bimorph harvester with tip mass reported in the literature. The flexibility of the method is demonstrated by studying the influence of partial electrode coverage on the generated power output. 相似文献
14.
K. Y. Sze L. Q. Yao Sung Yi 《International journal for numerical methods in engineering》2000,48(4):565-582
In Part I of the paper, a hybrid‐stress‐assumed natural strain eight‐node solid‐shell element immune to shear, membrane, trapezoidal, thickness and dilatational lockings has been developed. Moreover, the element computational cost is reduced by enforcing admissible sparsity in the flexibility matrix. In this part of the paper, the solid‐shell element is generalized to a piezoelectric solid‐shell element. Using the two solid‐shell elements, smart structures with segmented piezoelectric sensors and actuators can be conveniently modelled. A number of problems are studied and comparisons with other ad hoc element models for smart structure modelling are presented. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
15.
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
16.
A. A. Yazdani H. R. Riggs A. Tessler 《International journal for numerical methods in engineering》2000,47(11):1825-1840
The Penalized Discrete Least‐Squares (PDLS) stress recovery (smoothing) technique developed for two‐dimensional linear elliptic problems [1–3] is adapted here to three‐dimensional shell structures. The surfaces are restricted to those which have a 2‐D parametric representation, or which can be built‐up of such surfaces. The proposed strategy involves mapping the finite element results to the 2‐D parametric space whichdescribes the geometry, and smoothing is carried out in the parametric space using the PDLS‐based Smoothing Element Analysis (SEA). Numerical results for two well‐known shell problems are presented to illustrate the performance of SEA/PDLS for these problems. The recovered stresses are used in the Zienkiewicz–Zhu a posteriori error estimator. The estimated errors are used to demonstrate the performance of SEA‐recovered stresses in automated adaptive mesh refinement of shell structures. The numerical results are encouraging. Further testing involving more complex, practical structures is necessary. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
17.
Won I. Hong Jong H. Kim Yong H. Kim Sung W. Lee 《International journal for numerical methods in engineering》2001,52(7):747-761
A formulation for 36‐DOF assumed strain triangular solid shell element is developed for efficient analysis of plates and shells undergoing finite rotations. Higher order deformation modes described by the bubble function displacements are added to the assumed displacement field. The assumed strain field is carefully selected to alleviate locking effect. The resulting element shows little effect of membrane locking as well as shear locking, hence, it allows modelling of curved shell structures with curved elements. The kinematics of the present formulation is purely vectorial with only three translational degrees of freedom per node. Accordingly, the present element is free of small angle assumptions, and thus it allows large load increments in the geometrically non‐linear analysis. Various numerical examples demonstrate the validity and effectiveness of the present formulation. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
18.
Brian L. Kemp Chahngmin Cho Sung W. Lee 《International journal for numerical methods in engineering》1998,43(5):909-924
A set of four-node shell element models based on the assumed strain formulation is considered here. The formulation allows for changes in the shell thickness. As a result, the kinematics of deformation are described by purely vectorial variables, without using rotational angles. The present study investigates the use of bubble function displacements and the assumed strain field. Careful selection of the assumed strain terms generates an element whose order of numerical integration does not increase even when the bubble function displacements are added. Results for the four-node element without any bubble function terms show sensitivity to element distortion. Use of the bubble functions with a carefully chosen assumed strain field greatly improves element performance. © 1998 John Wiley & Sons, Ltd. 相似文献
19.
M. C. Ray 《International journal for numerical methods in engineering》2017,109(13):1804-1820
This paper is concerned with the development of mesh‐free models for the static analysis of smart laminated composite beams. The overall smart composite beam is composed of a laminated substrate composite beam and a piezoelectric layer attached partially or fully at the top surface of the substrate beam. The piezoelectric layer acts as the distributed actuator layer of the smart beam. A layer‐wise displacement theory and an equivalent single‐layer theory have been used to derive the models. Several cross‐ply substrate beams are considered for presenting the numerical results. The responses of the smart composite beams computed by the present new mesh‐free model based on the layer‐wise displacement theory excellently match with those obtained by the exact solutions. The mesh‐free model based on the equivalent single‐layer theory cannot accurately compute the responses due to transverse actuation by the piezoelectric actuator. The models derived here suggest that the mesh‐free method can be efficiently used for the numerical analysis of smart structures. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
20.
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