In the last few years, the rapid diffusion of components produced through additive manufacturing processes has boosted the research on design methodologies based on topology optimization algorithms. Structural topology optimization is largely employed since it permits to minimize the component weight and maximize its stiffness and, accordingly, optimize its resistance under structural loads. On the other hand, thermal topology optimization has been less investigated, even if in many applications, such as turbine blades, engines, heat exchangers, thermal loads have a crucial impact. Currently, structural and thermal optimizations are mainly considered separately, despite the fact that they are both present and coupled in components in service condition. In the present paper, a novel methodology capable of defining the optimized structure under simultaneous thermomechanical constraints is proposed. The mathematical formulation behind the optimization algorithm is reported. The proposed methodology is finally validated on literature benchmarks and on a real component, confirming that it permits to define the topology, which presents the maximized thermal and mechanical performance.

The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of hyperbolic type, in order to take into account the finite velocity of propagation of the density variations. We show that in this framework the condition on the conservation of the number of particles gives rise to a non-local boundary condition. We solve the partial differential equation relevant to the diffusion of particles by means of the separation of variables, and present how it is possible to obtain approximated eigenvalues contributing to the solution. The same problem is faced numerically by a finite difference algorithm. The time dependence of the surface density of adsorbed particles is deduced by means of the kinetic equation at the interface. The predicted non-monotonic behavior of the surface density versus the time is in agreement with experimental observations reported in the literature, and is related to the finite velocity of propagation of the density variations.

We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption phenomenon. For sake of simplicity, the analysis is performed by considering a sample in the shape of a slab limited by two perfectly blocking surfaces, in such a manner that the problem is one-dimensional in the space. Two cases are investigated. In the former, the initial distribution of the diffusing particles is assumed of gaussian type, centered around the symmetry surface in the middle of the sample. In the latter, the initial distribution is localized close to the limiting surfaces. In both cases, we show that the evolution toward to the equilibrium distribution is not monotonic. In particular, close to the limiting surfaces the bulk density of diffusing particles present maxima and minima related to the finite velocity of the diffusion process connected to the second order time derivative in the partial differential equation describing the evolution of the bulk density in the sample.

Hybrid rocket motors usually have an aft-mixing chamber in order to improve combustion efficiency. The presence of a sudden expansion at the exit of the fuel port determines the formation of vortices, whose vigourous burning may drive acoustic waves in the chamber. The shedding of vortices itself is then affected by the flow fluctuations, producing a well-known feedback loop. A reduced-order model, introduced by Matveev and Culick in 2003, is here used to analyze this phenomenon. It is assumed that vortex burning is localized in space and time, and a kicked oscillator model is utilized. A one-dimensional model proposed by the authors is used to determine the values of the eingenacoustic modes and corresponding damping coefficients. Numerical results are compared to experimental data

Computational models describing the behavior of complex physical systems are often used in the engineering design field to identify better or optimal solutions with respect to previously defined performance criteria. Multi-objective optimization problems arise and the set of optimal compromise solutions (Pareto front) has to be identified by an effective and complete search procedure in order to let the decision maker, the designer, to carry out the best choice. Four multi-objective optimization techniques are analyzed by describing their formulation, advantages and disadvantages. The effectiveness of the selected techniques for engineering design purposes is verified by comparing the results obtained by solving a few benchmarks and a real structural engineering problem concerning an engine bracket of a car.

The paper describes how to take into consideration the presence of transmissible loads in a topology optimization method based on optimality criteria. The optimization problem has been defined as a total potential energy maximization problem with stress, displacement or stiffness constraints. The final volume of the optimal structural configuration has not to be specified a priori and is a consequence of the imposed structural constraints. The implementation of the proposed method is quite simple and leads to the identification of well defined optimal structures. The results obtained by solving several benchmark problems are shown.

This paper proposes a novel numerical procedure to evaluate the shielding factor of ferromagnetic grid shields, coupling the thin-shell formulation with the multiple scale expansion homogenization method. This approach is applied to three typical configurations for magnetic field mitigation under dc and 50Hz sinusoidal supply conditions, considering nickel and iron alloys. The influence of the shield hole dimension is finally evaluated.

This paper presents a mathematical homogenization technique able to handle fine periodic structures in presence of magnetic saturable/hysteretic media. The modeling approach, based on the multiple scale expansion theory, enables the evaluation both of equivalent electric parameters and effective magnetization curves (or hysteresis loops). The results of the homogenization technique are validated by comparison with those provided by a standard finite element solution of a two-dimensional current driven problem defined on the heterogeneous domain.

This paper presents the application of a homogenisation technique, based on the multi-scale expansion theory, to the analysis of heterogeneous materials constituted of magnetic inclusions dispersed in a dielectric lattice. The role of the shape and dimensions of the inclusions is analysed with reference to the effective electromagnetic properties and energy losses. The investigation is extended to the influence of flux waveforms with harmonic distortion, focusing the attention on the energy loss dependency on the harmonic content.

In this paper, in the framework of a problem related to an elastic non homogeneous medium, we deal with a periodic coupled force (f(x)/ε ^α ) F⃗ (x/ε ) with intensity of order 1/ε α. The parameter ε is connected with the period of the non homogeneity of the medium and with the periodicity of the coupled force. The determination of the parameter α is the target of our study to obtain an effect in the microscopic equation. The homogenization technique is used in order to study the equation: - (∂ /∂ x_j ) (a_ijkh (x/ε ) e_kh (u⃗^ε ,α )) = (f(x)/ε ^α ) F_i (x/ε ) + G_i (x,x/ε ) , where G i (x,x/ε) is the volume applied force. The limit, when ε → 0, of u⃗^ε ,α (x) , in the sense of two scale convergence, is (u⃗^0,α (x), u⃗^1,α (x,y)) and the microscopic equation becomes: - (∂ /∂ y_j ) (a_ijkh (y) e_khx (u⃗^0,α (x))) - (∂ /∂ y_j ) (e_khy (u⃗^1,α (x,y))) = f(x) F_i (y) if α = 1, - (∂ /∂ y_j ) (a_ijkh (y) e_khx (u⃗^0,α (x)) + e_khy (u⃗^1,α (x,y))) = 0 if 0 > α > 1. When α < 1 the solutions are not uniformly bounded respect to ε.

This paper deals, in the framework of homogenization theory, with a problem arising in civil engineering. A periodic masonry structure is considered where the constitutive materials are bricks and mortar. Global mechanical properties of the masonry are derived on the basis of the properties of materials. The study of the elastic properties of the homogenized masonry uses stratified homogenization techniques. The relations of the elastic homogenized coefficients are obtained, by variational formulation, starting from the elasticity equations and are solved by the finite-elements method. This technique is applied to some cases treated by other authors and the results are compared.

In this paper, we deal with the steady-state acoustic wave equation in the space ℝ 3 diffracted by an obstacle made by an inhomogeneous medium and located in a bounded domain. The inhomogeneity of the medium depends on a parameter ε > 0. If the solution u ε converges to a solution u 0 of the limit problem as ε → 0, as in the homogenization process, then we can use the two-scale convergence method to study the convergence of the gradient.

A mathematical homogenization technique is applied to the computation of eddy currents in strip-wound amorphous cores. The results are compared with a standard finite-element (FE) solution of a test problem. The method is applied to the analysis of an amorphous core in a frequency range up to 1 MHz, with main emphasis on energy loss prediction.

The paper deals with the application of the homogenization technique to the electromagnetic analysis of non-homogeneous materials composed of grains bounded by a layer whose electrical and magnetic characteristics are sensibly different. The investigation is performed by comparing local and integral quantities, provided by the proposed approach, with the results given by a standard finite element solution, which requires a significantly higher processing time. The influence of different geometrical and constitutive parameters and the merits and limits of the method are finally discussed.

In this paper, we consider a family of scattering problems in perforated unbounded domains Ωε. We assume that the perforation is contained in a bounded reg ion and that the holes have a ‘critical’ size. We study the asymptotic behaviour of the outgoing solu tions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions. Problemas de difracci ón en un dominio con peque ños agujeros. Resumen. En este artı́culo consideramos una familia de problemas de d ifracción en un dominioΩε no limitado y perforado. Suponemos que las perforaciones es tán contenidas en una región limitada y que los agujeros tengan una talla crı́tica. Estudiamos el co mportamiento asintótico de las soluciones que emergen del problema estacionario de difracción y prob am s que en la ecuación lı́mite, aparece un término nuevo. Finalmente, obtenemos algunos resultados de convergencia para las frecuencias y las soluciones de difracción.

In this paper, we consider a family of scattering problems in perforated unbounded domains ". We assume that the perforation is contained in a bounded region and that the holes have a 'critical' size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions. Problemas de difracci ´ on en un dominio con peque ˜ nos agujeros. Resumen. En este art´ iculo consideramos una familia de problemas de difraccion en un dominio " no limitado y perforado. Suponemos que las perforaciones estan contenidas en una region limitada y que los agujeros tengan una talla cr´ itica. Estudiamos el comportamiento asintotico de las soluciones que emergen del problema estacionario de difraccion y probamos que en la ecuacion l´ imite, aparece un termino nuevo. Finalmente, obtenemos algunos resultados de convergencia para las frecuencias y las soluciones de difraccion.

Two-scale models for reinforced concrete, where the large-scale problems are defined in terms of Euler–Bernoulli beam and Kirchhoff–Love plate models, are constructed. The subscale problem on the Representative Volume Element (RVE) is correspondingly outlined as finding the response of the three-dimensional RVE comprising plain concrete continuum, reinforcement bars and the bond between them. The boundary region of the periodic mesh is modelled with special solid elements, which allow for prescribing the macroscopic input via strongly periodic boundary conditions in an effective way. The effective response of the reinforced concrete RVEs of different sizes subjected to tension and pure bending is investigated for both effective beam and plate models. A series of experiments on reinforced concrete panels subjected to bending and membrane loads is simulated, and the effective moment–curvature response is studied. Within the developed framework, an arbitrary macroscopic loading in terms of membrane strains and curvatures can be prescribed on the RVE, and the corresponding effective response is obtained, making the proposed formulation feasible for future use in an FE2 scheme.

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