Liu Zheng-xing

Spherical-symmetric steady-state response of piezoelectric spherical shell under external excitation

Spherical-symmetric stead-state response problem of piezoelectric spherical shell in the absence of body force and free charges is discussed. The steady-state response solutions of mechanical displacement, stresses, strains, potential and electric displacement were derived from constitutive relations, geometric and motion equations for the piezoelectric medium under external excitation ( i. e. applied surface traction and potential) in spherical coordinate system. As an application of the general solutions, the problem of an elastic spherical shell with piezoelectric actuator and sensor layers was solved. The results could provide good theoretical basis for the spherical symmetric dynamic control problem of piezoelectric intelligent structure. Furthermore, the solutions can serve as reference for the research of general dynamic control problem.

Topology optimization design of continuum structures under stress and displacement constraints

Topology optimization design of continuum structures that can take account of stress and displacement constraints simultaneously is difficult to solve at present. The main obstacle lies in that, the explicit function expressions between topological variables and stress or displacement constraints can not be obtained using homogenization method or variable density method. Furthermore, large quantities of design variables in the problem make it hard to deal with by the formal mathematical programming approach. In this paper, a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing. Moreover, the approximate, explicit expressions are given between topological variables and stress or displacement constraints. The problem is well solved by using dual programming approach, and the proposed element deletion criterion implements the inversion of topology variables from the discrete to the continuous. Numerical examples verify the validity of proposed method.

Large deflection analysis of thin elastic shells by a hybrid stress method

Abstract Based on the incremental complementary energy principle, a hybrid stress model is developed for the geometrical nonlinear analysis of plates and shells. According to the compatibility of interior and boundary displacements for an element, and the equilibrium of stresses at the interior of the element, an inconsistent model which partially satisfies the stress equilibrium equation is utilized in the present paper, and a three node, 15 degree of freedom, triangular shallow shell element is established. Formulas are derived in the updated Lagrangian coordinate system. Numerical examples demonstrate that the assumed hybrid stress model is very efficient.

ANALYSIS OF BEAMS WITH PIEZOELECTRIC ACTUATORS

Based on the two-dimensional constitutive relationships of the piezoelectric material, an analytical solution for an intelligent beam excited by a pair of piezoelectric actuators is derived. With the solution the force and moment generated by two piezoelectric actuators and a pair of piezoelectric actuator/sensor are obtained. Examples of a cantilever piezoelectric laminated beam or a simply supported piezoelectric laminated beam, applied with voltages, are given.

ACTIVE CONTROL OF THE PIEZOELASTIC LAMINATED CYLINDRICAL SHELL'S VIBRATION UNDER HYDROSTATIC PRESSURE *

The control of the piezoelastic laminated cylindrical shells vibration under hydrostatic pressure was discussed. From Hamiltons principle nonlinear dynamic equations of the piezoelastic laminated cylindrical shell were derived. Based on which, the dynamic equations of a closed piezoelastic cylindrical shell under hydrostatic pressure are obtained. An analytical solution was presented for the case of vibration of a simply supported piezoelastic laminated cylindrical shell under hydrostatic pressure. Using velocity feedback control, a model for active vibration control of the laminated cylindrical shell with piezoelastic sensor/actuator is established. Numerical results show that, the static deflection of the cylindrical shell can be changed when voltages with suitable value and direction are applied on the piezoelectric layers. For the dynamic response problem of the system, the larger the gain is, the more the vibration of the system is suppressed in the vicinity of the resonant zone. This presents a potential way to actively reduce the harmful effect of the resonance on the system and verify the feasibility of the active vibration control model.

Plane infinite analytical element and hamiltonian system

It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate. All governing equations were transformed into the Hamiltonian system. The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element. This new element, like a super finite element, can be combined with commonly used finite elements. The proposed method was verified by numerical case studies. The results show that the preparation work is very simple, the infinite analytical element has a high precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.

Element functions of discrete operator difference method

The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.