Design methodology of piezoelectric energy-harvesting skin using topology optimization

Abstract This paper describes a design methodology for piezoelectric energy harvester s that thinly encapsulate the mechanical devices and expl oit resonances from higher- order vibrational modes. The direction of polarization determines the sign of the pi ezoelectric tensor to avoid cancellations of electric fields from opposite polarizations in the same circuit. The resultant modified equations of state are solved by finite element method (FEM). Com- bining this method with the solid isotropic material with penalization (SIMP) method for piezoelectric material, we have developed an optimization methodology that optimizes the piezoelectric material layout and polarization direc- tion. Updating the density function of the SIMP method is performed based on sensitivity analysis, the sequen- tial linear programming on the early stage of the opti- mization, and the phase field method on the latter stage

Improving rockbolt design in tunnels using topology optimization

Finding an optimum reinforcement layout for underground excavation can result in a safer and more economical design, and is therefore highly desirable. Some works in the literature have applied topology optimization in tunnel reinforcement design in which reinforced rock is modeled as homogenized isotropic material. Optimization results, therefore, do not clearly show reinforcement distributions, leading to difficulties in explaining the final outcomes. To overcome this deficiency, a more sophisticated modeling technique in which reinforcements are explicitly modeled as truss elements embedded in rock mass media is used. An optimization algorithm extending the solid isotropic material with penalization method is introduced to seek for an optimal bolt layout. To obtain the stiffest structure with a given amount of reinforced material, external work along the opening is selected as the objective function with a constraint on the volume of reinforcement. The presented technique does not depend on material models used for rock and reinforcements and can be applied to any material model. Nonlinear material behavior of rock and reinforcement is considered in this work. Through solving some typical examples, the proposed approach is proved to enhance the conventional reinforcement design and provide clear and practical reinforcement layouts.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.