Table of Contents Entry This review covers energy harvesting technologies associated with piezoelectric materials along with the sub-classes of pyroelectrics and ferroelectrics. These properties are often present in the same material, providing the intriguing prospect of a material that can harvest energy from multiple sources including vibration, thermal fluctuations and light.

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Uncertainty is an important consideration in structural design and optimization to produce robust and reliable solutions. This paper introduces an efficient and accurate approach to robust structural topology optimization. The objective is to minimize expected compliance with uncertainty in loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. This new approach is analogous to a multiple load case problem where load cases and weights are derived analytically to accurately and efficiently compute expected compliance and sensitivities. Illustrative examples using a level set based topology optimization method are then used to demonstrate the proposed approach. Nomenclature

Robust topology optimization has long been considered computationally intractable as it combines two highly expensive computational strategies. This paper considers simultaneous minimization of expectancy and variance of compliance in the presence of uncertainties in loading magnitude, using exact formulations and analytically derived sensitivities. It shows that only a few additional load cases are required, which scales in polynomial time with the number of uncertain load cases. The approach is implemented using the level set topology optimization method. Shape sensitivities are derived using the adjoint method. Several examples are used to investigate the effect of including variance in robust compliance optimization. λ = Lagrange multiplier µ i = mean magnitude of uncertain load i σ i = standard deviation of uncertain load i € σ = covariance Ω = design domain Ω S = structural domain

This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of nonlevel-set design variables.

This paper presents an arrangement of bistable composites combined with piezoelectrics for broadband energy harvesting of ambient vibrations. These non-linear devices have improved power generation over conventional resonant systems and can be designed to occupy smaller volumes than magnetic cantilever systems. This paper presents results based on optimization of bistable composites that enables improved electrical power generation by discovering the optimal configurations for harvesting based on the statics of the device. The optimal device aspect ratio, thickness, stacking sequence, and piezoelectric area are considered. Increased electrical output is found for geometries and piezoelectric configurations, which have not been considered previously.

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