This article presents a model to simulate the behavior of a magnetic shape memory alloy while harvesting vibratory energy. In this type of energy harvester, magnetic shape memory alloy element is placed in the air gap of a ferromagnetic core which conducts the magnetic flux. Two apparent coils are wound around a ferromagnetic core: one to produce bias magnetic field by passing a rectified electric current and the other to serve as an energy pickup coil. Applying compressive time-variant strain field to magnetic shape memory alloy element changes its dimensions and magnetic properties as well. Presence of the bias magnetic field returns magnetic shape memory alloy element to its initial state while removing the load. Changes in magnetic properties of magnetic shape memory alloy will change the magnetic flux passing through the pickup coil and will produce an alternative voltage in that coil based on the Faraday’s law of induction consequently. In the modeling strategy, magnetic behavior of magnetic shape memory alloy element during operation is obtained by solving the thermodynamic-based constitutive equation numerically and the energy harvesting process modeled with equivalent magnetic and electric circuits. By varying the system parameters in the model, output voltage and power changes are reported accordingly.

Topology optimization (TO) of engineering products is an important design task to maximize performance and efficiency, which can be divided into two main categories of gradient-based and non-gradient-based methods. In recent years, significant attention has been brought to the non-gradient-based methods, mainly because they do not demand access to the derivatives of the objective functions. This property makes them well compatible to the structure of knowledge in the digital design and simulation domains, particularly in Computer Aided Design and Engineering (CAD/CAE) environments. These methods allow for the generation and evaluation of new evolutionary solutions without using the sensitivity information. In this work, a new non-gradient TO methodology using a variation of Simulated Annealing (SA) is presented. This methodology adaptively adjusts newly-generated candidates based on the history of the current solutions and uses the crystallization heuristic to smartly control the convergence of the TO problem. If the changes in the previous solutions of an element and its neighborhood improve the results, the crystallization factor increases the changes in the newly random generated solutions. Otherwise, it decreases the value of changes in the recently generated solutions. This methodology wisely improves the random exploration and convergence of the solutions in TO. In order to study the role of the various parameters in the algorithm, a variety of experiments are conducted and results are analyzed. In multiple case studies, it is shown that the final results are well comparable to the results obtained from the classic gradient-based methods. As an additional feature, a density filter is added to the algorithm to remove discontinuities and gray areas in the final solution resulting in robust outcomes in adjustable resolutions.

This chapter is related to several aspects of optimization problems in engineering. Engineers usually mathematically model a problem and create a function that must be minimized, like cost, required time, wasted material, etc. Eventually, the function must be maximized. This function has different names in the literature: objective function, cost function, etc. We will refer to it in the chapter as objective function. There is a wide range of possibilities for the problems and they can be classified in different ways. At first, the values of the parameters can be continuous, discrete (integers), cyclic (angles), intervals, and combinatorial. The result of the objective function can be continuous, discrete (integers) or intervals. One very difficult class of problems have continuous parameters and discrete objective function, this type of objective function has very weak sensibility. This chapter shows the versatility of the simulated annealing showing that it can have different possibilities of parameters and objective functions.

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