Eight-node Solid-shell Element Research Articles

A novel hybrid-stress method using an eight-node solid-shell element for nonlinear thermoelastic analysis of composite laminated thin-walled structures

Composite laminated thin-walled structures, widely used in high-speed aircrafts, undergo a complex thermal–mechanical coupling environment. Geometrical nonlinearities with a thermal effect bring significant challenge to finite element analysis of structures. In this paper, a novel hybrid-stress method based on the solid-shell element is proposed for nonlinear thermoelastic analysis. An eight-node solid-shell element (CSSH8) is developed based on the assumed natural strain method and hybrid-stress formulations to overcome various locking problems and achieve an effective 3D simulation for structures with a large span-thickness ratio. The Green–Lagrange displacement-strain relation is selected to take the geometrical nonlinearities into account. The modified generalized laminate constitutive model is extended to consider both the thermal expansion and temperature-dependent material properties. A temperature variation along the laminate thickness can also be assumed in the constitutive model. Nonlinear thermoelastic equilibrium equations are derived using the Hellinger–Reissner variational principle, in which five different coupling cases for thermal–mechanical loads can be fully involved. Numerical examples demonstrate that the proposed method with CSSH8 element is insensitive to various distorted meshes and numerically robust to pass the buckling point; meanwhile large step sizes can be achieved in the path-following nonlinear thermoelastic analysis.

Smoothed finite element method implemented in a resultant eight-node solid-shell element for geometrical linear analysis

A smoothed finite element method formulation for the resultant eight-node solid-shell element is presented in this paper for geometrical linear analysis. The smoothing process is successfully performed on the element mid-surface to deal with the membrane and bending effects of the stiffness matrix. The strain smoothing process allows replacing the Cartesian derivatives of shape functions by the product of shape functions with normal vectors to the element mid-surface boundaries. The present formulation remains competitive when compared to the classical finite element formulations since no inverse of the Jacobian matrix is calculated. The three dimensional resultant shell theory allows the element kinematics to be defined only with the displacement degrees of freedom. The assumed natural strain method is used not only to eliminate the transverse shear locking problem encountered in thin-walled structures, but also to reduce trapezoidal effects. The efficiency of the present element is presented and compared with that of standard solid-shell elements through various benchmark problems including some with highly distorted meshes.

A hybrid-stress solid-shell element for non-linear analysis of piezoelectric structures

This paper presents eight-node solid-shell elements for geometric non-linear analyze of piezoelectric structures. To subdue shear, trapezoidal and thickness locking, the assumed natural strain method and an ad hoc modified generalized laminate stiffness matrix are employed. With the generalized stresses arising from the modified generalized laminate stiffness matrix assumed to be independent from the ones obtained from the displacement, an extended Hellinger-Reissner functional can be derived. By choosing the assumed generalized stresses similar to the assumed stresses of a previous solid element, a hybrid-stress solid-shell element is formulated. The presented finite shell element is able to model arbitrary curved shell structures. Non-linear numerical examples demonstrate the ability of the proposed model to analyze nonlinear piezoelectric devices.

A model-adaptive hanging node concept based on a new non-linear solid-shell formulation

In this contribution we propose an innovative approach to automatically refine shell finite element meshes in thickness direction. The procedure employs a new eight-node solid-shell element formulation based on the concept of reduced integration with hourglass stabilization. Apart from the important advantages of computational efficiency and robustness this element formulation offers the possibility to work with a variable mesh density in thickness direction. In the present paper we suggest an adaptive approach using the hanging node concept to avoid additional mesh distortion. Among different stress- and strain-based error criteria the warping of the cross-section and the residual error in the solution of the strong form of the balance of linear momentum have been proven to be suitable error measures. The former represents the deviation of the realistically non-linear dependence of the characteristic strain coefficient from its corresponding linear distribution. Applications show that the mesh refines, as expected, in loading domains, in the neighbourhood of bearings or regions with strongly accumulating inelastic deformation. On the other hand, the discretization remains rather coarse in uncritical parts of the structure which decreases the computational effort noticeably.

A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part I-geometrically linear applications

Accuracy and efficiency are the main features expected in finite element method. In the field of low-order formulations, the treatment of locking phenomena is crucial to prevent poor results. For three-dimensional analysis, the development of efficient and accurate eight-node solid-shell finite elements has been the principal goal of a number of recent published works. When modelling thin- and thick-walled applications, the well-known transverse shear and volumetric locking phenomena should be conveniently circumvented. In this work, the enhanced assumed strain method and a reduced in-plane integration scheme are combined to produce a new eight-node solid-shell element, accommodating the use of any number of integration points along thickness direction. Furthermore, a physical stabilization procedure is employed in order to correct the element's rank deficiency. Several factors contribute to the high computational efficiency of the formulation, namely: (i) the use of only one internal variable per element for the enhanced part of the strain field; (ii) the reduced integration scheme; (iii) the prevention of using multiple elements' layers along thickness, which can be simply replaced by any number of integration points within a single element layer. Implementation guidelines and numerical results confirm the robustness and efficiency of the proposed approach when compared to conventional elements well-established in the literature. Copyright © 2004 John Wiley & Sons, Ltd.

MODELLING SMART STRUCTURES WITH SEGMENTED PIEZOELECTRIC SENSORS AND ACTUATORS

In this paper, a number of finite element models have been developed for comprehensive modelling of smart structures with segmented piezoelectric sensing and actuating patches. These include an eight-node solid-shell element for modelling homogeneous and laminated host structures as well as an eight-node solid-shell and a four-node piezoelectric membrane elements for modelling surface bonded piezoelectric sensing and actuating patches. To resolve the locking problems in these elements and improve their accuracy, assumed natural strain and hybrid stress formulations are employed. Furthermore, piezoelectric patches are often coated with metallization. The concept of electric nodes is introduced that can eliminate the burden of constraining the equality of the electric potential for physical nodes lying on the same metallization. A number of problems are studied by the developed finite element models and comparisons with other ad hoc element models are presented.

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

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.

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

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.