A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators: Bending and free vibrations

This paper addresses the bending and free vibrations of multilayered cylindrical shells with piezoelectric properties using a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elasticity theory. In the present 3D axisymmetric model, the equations of motion are expressed by expanding the displacement field using Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.     

Multiobjective optimization of a two-piece aluminum beverage bottle considering tactile sensation of heat and embossing formability

This paper deals with a multiobjective optimization of a screw-top beverage bottle for hot vending. The bottle body has temperate touch feeling and can be embossed easily by axially imposing a cylindrical tube die with rib-shaped inner surface on the outer surface of the bottle body. Initially, a contact nonlinear analysis of fingers grasping the bottle is carried out, and the amount of heat transmitted from the hot bottle to the flesh of the finger is then calculated to evaluate the hot touch feeling. Meanwhile, the simulation of the rib-shape embossing process of the bottle body is performed to evaluate the embossing formability of different rib shape designs. Finally, using response surface approximation method and weighted sum approach, a multiobjective optimization on the shape of the rib is performed to obtain temperate touch feeling as well as better embossing formability. The amount of heat transmitted from the optimized rib-shape embossed bottle decreased at least 30% as compared with that of the regular bottle.     

An exact solution for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends

In this paper, a new exact solution based on the classical shell theory (CST) for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends is proposed. The present exact solution can be summed up in the following steps: Firstly, the displacement functions are constructed by the governing differential equations with the exact closed form solutions; Then, the artificial spring technology is introduced to simulate the general boundary conditions of the two end edges of shell; Thirdly, the equation for natural frequencies is obtained by means of the method of reverberation-ray matrix (MRRM); Lastly, the vibration results are presented by the modified golden section search (MGSS) algorithm. By comparing the present method with published papers, the accuracy of present method is verified. On the basis of that, some new exact nature frequencies and mode shapes of the cross-ply laminated composite cylindrical shells with various classical boundary conditions and elastic restraints are performed and they can be served as the benchmark data for the future.