Laminated piezocomposite energy harvesters (LAPEHs) are multilayer arrangements of piezoelectric and nonpiezoelectric materials. Multiple materials and physics, and dynamic analysis need to be considered in their design. Usually these devices are designed for harmonic excitation; however, they are subjected to other types of excitations. Thus, a novel topology optimization formulation is developed for designing LAPEHs that considers a combination of harmonic and transient optimization problems with the aim of designing the so-called "multi-entry" devices in which the power generated is the same for different types of excitation. LAPEHs are modeled by the finite element method, and the material model used for the piezoelectric layer is based on penalization and polarization model who controls material distribution and corresponding polarization. To optimize the RLC circuit, a novel linear interpolation model of coupled electrical impedance is also introduced to consider different magnitudes of the coupled impedance. The topology optimization problem seeks to maximize the active power generated by the LAPEH at its RLC circuit, to minimize its response time measured as the slope of the power versus time curve, and to maximize its stiffness. Numerical examples are shown to illustrate the potential of the method.

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Functionally graded materials (FGMs) are a new class of bio-inspired composite materials made from different material phases, in which their volume fraction changes gradually towards a particular direction. Accordingly, continuous changes in the composition, microstructure and porosity of the graded materials results in material properties gradients; for this reason, the material properties move smoothly and continuously from one surface to another, eliminating the interface problem. Hence, with appropriate design, FGMs can develop better properties than their homogeneous counterpart due to their better designability. One potential employment of FGMs is as damper or energy absorber in dynamic applications, in which optimization techniques such as the topology optimization method (TOM) can contribute to a better performance in relation to a non-optimized design. In this chapter, functionally graded structures are designed with and without the TOM in order to explore the advantages of the FGM concept in low-velocity impact condition, which is a special case in the world of dynamic analysis, and has interest for designing machinery parts and components.

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The modeling of heat transfer phenomena in thermal systems has been extensively explored in industry and academia by using the finite element method (FEM) with commercial software. However, when the thermal problem introduces complexities in geometry and physics, the availability of licenses for high-performance computing could represent a limitation to achieving results in a reasonable time. Hence, finite element analysis (FEA) using open-source software (OSS) becomes a prominent candidate in this case. Therefore, multiple open-source tools are integrated into this work to solve the heat transfer equation, including conduction, convection, and radiation. Several geometrically complex heat sinks commonly used in the electronics industry are considered application examples. The performance of parallel computing is assessed in terms of processing time. The finite element solution engine is built by implementing the energy balance equations in their weak formulation in Firedrake, using its solver PETSc, the mesh generator GMSH and the post-processor Paraview, thus creating a fully OSS-based Python framework. Finally, the results are verified with commercial software for different case studies, and its potential to be extended to other fields of engineering is evident.