![]() ![]() Such assumptions are good enough in thin plates or in the case of homogeneous or isotropic materials. All plate bending theories such as Kirchhoff–Love plate theory or high-order plate theories assume a prespecified displacement distribution along the plate thickness. The bending behavior of thick or moderately thick plates is considerably affected by shear deformations, especially when complex materials such as laminated composites or FGM materials are considered. ![]() Recent technologies use additive manufacturing to produce FGM materials, and consequently, the FGM parts with multi-directional material variations are realistic today. Therefore, parametric study is one important step in the optimum design of FGM parts. After that, a parametric analysis is needed to assess the effect of these material distribution parameters on the mechanical performance of the whole component. These models are based on one or more controlling parameters that determine the materials distributions. Here, different models are used to describe the materials distributions over the plate volume. The design of FGM materials consists of an accurate determination of spatial distribution of concentration (or volume fraction) of constituents. This feature makes the FGM the ideal choice in severe thermal environments and makes it possible to have a part with the pure metallic phase at one point to satisfy strength and the pure ceramic phase at another point to resist again high temperature. In contrast, the gradual variation of material properties in FGM materials prevents from such behaviors. In traditional composite materials, the mechanical properties evolve sharply at the interface of different phases, and this leads to high interfacial stresses and in many times the origin of failure. The new class of composite materials in which the mechanical properties evolve continuously in space is known as Functionally Graded Materials (FGM). In the present work, some sample examples in 4D and 5D computational spaces are solved, and the results are presented. Therefore, the PGD makes it possible to handle high-dimensional problems efficiently. Due to the curse of dimensionality, solving a high-dimensional parametric problem is considerably more computationally intensive than solving a set of one-dimensional problems. In the PGD technique, the field variables are separated to a set of univariate functions, and the high-dimensional governing equations reduce to a set of one-dimensional problems. A parametric analysis of FGM materials is especially useful in material design and optimization. ![]() In the present work, material gradation is considered in one, two and three directions, and 3D heat transfer and theory of elasticity equations are solved to have an accurate temperature field and be able to consider all shear deformations. The FGMs have important applications in space technologies, especially when a part undergoes an extreme thermal environment. In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). ![]()
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