K. Y. Sze

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

A Micro-mechanics Model for Imperfect Interface in Dielectric Materials

The interface between two dielectric bodies is considered imperfect if there are defects (micro-voids and micro cracks) present on the interface. For such interface, the perfect continuity condition across the interface is no longer valid and its use in analysis becomes questionable. To account for this imperfection, we propose a micro-mechanics model based on self-consistent scheme, leading to the establishment of a constitutive relationship between the electric displacement and potential discontinuity across the imperfect interface.

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

Two-dimensional contact on a piezoelectric half-space

Abstract Due to their intrinsic electro-mechanical coupling effect, piezoelectric materials have been widely used in industry. In the present paper, stress and electrical field distributions in a piezoelectric half-plane under contact load at the surface are considered. Since a piezoelectric material is intrinsically anisotropic, stress analysis has been impeded by the complexity raised by too many material constants. Hereby, Strohs formalism is applied in the present study to overcome this difficulty. The solution for a concentrated force and charge acting on the boundary of the half-space, the Green function, is obtained in a neat form. The non-slip and slip indentor contacts on the piezoelectric half-space are also formulated.

Non-fragile H∞ vibration control for uncertain structural systems

The paper deals with the robust non-fragile H∞ control problem for uncertain structural systems with additive controller gain variations. The parameter uncertainties for the mass, damping and stiffness of the structural systems are unknown but norm bounded. Based on the H∞ control theory and a linear matrix inequality formulation, a new method for designing a robust state-feedback control law is presented. The objective is to reduce the disturbance on the controlled output to a prescribed level for all admissible parametric uncertainties and controller gain variations. A four-degree-of-freedom building model subject to seismic excitation is used to illustrate the effectiveness of the approach through simulation.

AN EXPLICIT HYBRID STABILIZED EIGHTEEN-NODE SOLID ELEMENT FOR THIN SHELL ANALYSIS

In this paper, the explicit hybrid stabilization method is employed to formulate stabilization vectors for the uniformly reduced integrated eighteen-node solid element. An assumed contravariant stress is devised based on the strain associated with the commutable mechanisms of a geometrically regular element. It will be seen that the stabilization vectors can be derived and programmed explicitly without resorting to numerical integration loops. Admissible matrix formulation is employed in evaluating the flexibility matrix which becomes diagonal and thus induces no inversion cost. The element accuracy is comparable with other state-of-the-art nine-node shell and eighteen-node solid elements. FORTRAN subroutines for constructing the stabilization vectors are presented.

AN EFFICIENT QUADRILATERAL PLANE ELEMENT WITH DRILLING DEGREES OF FREEDOM USING ORTHOGONAL STRESS MODES

Abstract In this paper, a mixed quadrilateral plane element with drilling degrees of freedom using Allmans interpolation scheme is developed. The assumed stress space includes three constant stress modes and four quasi-linear stress modes which are equilibrating for regular element geometry. Owing to the intrinsic orthogonality of the constant and higher order stress modes, the element is particularly efficient. Only a 4 × 4 symmetry matrix is required to be inverted while no incompatible displacement modes are involved. The element has two spurious kinematic modes which, however, can effectively be suppressed by using two very simple stabilization matrices. A number of popular benchmark problems are examined and the accuracy achieved is very satisfactory.

A novel hybrid finite element analysis of bimaterial wedge problems

Abstract An assumed hybrid-stress finite element model together with a new super singular wedge-tip element with numerical eigensolutions is developed to study the bimaterial wedge/notch problems. The establishment of the super wedge-tip element consists of (1) a finite element method-based eigenanalysis is developed and applied to determine the order of the stress singularity and the angular dependences of the stress and displacement fields, (2) these fields are subsequently used to develop a finite element surrounding the wedge tip. To demonstrate the validity of the method, three types of the bimaterial wedge problems are examined and compared with analytical/referenced solutions. The high accuracy and general applicability of the present technique are shown.

H∞ disturbance attenuation for uncertain mechanical systems with input delay

The paper deals with the robust H disturbance attenuation problem for uncertain mechanical systems with input delay. The parameter uncertainties for the mass, damping and stiffness matrices take an additive a priori norm-bounded form. The time delay for the input is time-invariant but has a known constant bound. A robust static H state-feedback controller is designed to attenuate the disturbance on the controlled output to a prescribed level for all admissible parameter uncertainties and input delay. The design approach is formulated in terms of the feasibility of certain delay-dependent linear matrix inequalities. A numerical example is employed to illustrate the effectiveness of the approach.

Design of non-fragile H∞ controller for active vehicle suspensions

In this paper we present an approach to design the non-fragile H ∞ controller for active vehicle suspensions. A quarter-car model with active suspension system is considered in this paper. By suitably formulating the sprung mass acceleration, suspension deflection and tire deflection as the optimization object and considering a priori norm-bounded controller gain variations, the non-fragile state-feedback H ∞ controller can be obtained by solving a linear matrix inequality. The designed controller not only can achieve the optimal performance for active suspensions but also preserves the closed-loop stability in spite of the controller gain variations.