A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part II?smart structure modelling

Sze, K. Y.; Yao, Lin; Yi, Sung

doi:10.1002/(sici)1097-0207(20000610)48:4<565::aid-nme890>3.0.co;2-u

Cited by 54 publications

(57 citation statements)

References 24 publications

(15 reference statements)

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“…The semicircular ring shell is a popular example for the dynamic analysis of piezoelectric curved structures and may be found in [19,17,15]. In the geometrically linear case the presented element verifies well known results form the literature.…”

Section: Semicircular Ring Shellsupporting

confidence: 75%

“…10 shows the tip displacement versus time. For this geometrically linear example the comparison with Sze et al [17] confirms a good agreement. In [17] the electric field in thickness direction is approximated as constant, whereas in the present element the electric field is approximated as a bilinear function in thickness direction, which is necessary to pass the out of plane bending patch test.…”

Section: Semicircular Ring Shellsupporting

confidence: 74%

“…The layers are glued together, where the polarized directions are opposite in X 3 direction. Here we consider the finite element mesh introduced by Sze et al [17], where the mesh distortion is described by the parameter s. The system is loaded by a unit Voltage through the thickness, which produces a constant electric field of E 3 = 10 3 V/m. An analytical solution is proposed by Tzou [42], who considered an Euler-Bernoulli beam theory.…”

Section: Bimorphmentioning

confidence: 99%

“…Hybrid and mixed approaches are also presented in [30,31,16,17]. Miranda and Ubertini [30] discuss the fully compatible approach in comparison to a hybrid approach.…”

Section: Introductionmentioning

confidence: 99%

“…The degenerated variational principles are employed to the finite element formulation. Sze and Yao [16,17] proposed a hybrid finite element shell formulation for smart structures modelling. In [16,17] three fields, the stress field, the displacements, and the electric potential are considered in the variational formulation, where the electric potential is assumed to be linear through the shell thickness.…”

Section: Introductionmentioning

confidence: 99%

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A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

Klinkel

Wagner

2005

Int. J. Numer. Meth. Engng

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This paper is concerned with a geometrically nonlinear solid shell element to analyze piezoelectric structures. The finite element formulation is based on a variational principle of the Hu-Washizu type and includes six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has 8 nodes with 4 nodal degrees of freedoms, 3 displacements and the electric potential. A bilinear distribution through the thickness of the independent electric field is assumed to fulfill the electric charge conservation law in bending dominated situations exactly. The presented finite shell element is able to model arbitrary curved shell structures and incorporates a 3D-material law. A geometrically nonlinear theory allows large deformations and includes stability problems. Linear and nonlinear numerical examples demonstrate the ability of the proposed model to analyze piezoelectric devices.

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Section: Semicircular Ring Shellsupporting

confidence: 75%

Section: Semicircular Ring Shellsupporting

confidence: 74%

Section: Bimorphmentioning

confidence: 99%

“…Hybrid and mixed approaches are also presented in [30,31,16,17]. Miranda and Ubertini [30] discuss the fully compatible approach in comparison to a hybrid approach.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

Klinkel

Wagner

2005

Int. J. Numer. Meth. Engng

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A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I?solid-shell element formulation

Sze

Yao

2000

Int. J. Numer. Meth. Engng.

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145

114

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SUMMARYIn the recent years, solid-shell "nite 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 be envisioned. 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 e$cient than the conventional hybrid elements by adopting orthogonal-assumed stress modes and enforcing admissible sparsity in the #exibility matrix. Popular benchmark tests are exercised to illustrate the e$cacy of the elements. In Part II of the paper, the element will be generalized for smart structure modelling by including the piezoelectric e!ect.

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Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control

Tan

Vu‐Quoc

2005

Int. J. Numer. Meth. Engng

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SUMMARYIn this paper, we present an optimal low-order accurate piezoelectric solid-shell element formulation to model active composite shell structures that can undergo large deformation and large overall motion. This element has only displacement and electric degrees of freedom (dofs), with no rotational dofs, and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out-of-plane bending). The combination of the present optimal piezoelectric solid-shell element and the optimal solid-shell element previously developed allows for efficient and accurate analyses of large deformable composite multilayer shell structures with piezoelectric layers. To make the 3-D analysis of active composite shells containing discrete piezoelectric sensors and actuators even more efficient, the composite solid-shell element is further developed here. Based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle, the in-plane and out-of-plane bending behaviours are improved via a new and efficient enhancement of the strain tensor. Shear-locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. We also present an optimal-control design for vibration suppression of a large deformable structure based on the general finite element approach. The linear-quadratic regulator control scheme with output feedback is used as a control law on the basis of the state space model of the system. Numerical examples involving static analyses and dynamic analyses of active shell structures having a large range of element aspect ratios are presented. Active vibration control of a composite multilayer shell with distributed piezoelectric sensors and actuators is performed to test the present element and the control design procedure.

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A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part II?smart structure modelling

Cited by 54 publications

References 24 publications

A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I?solid-shell element formulation

Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control

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