Development of consistent theories of functionally graded plates

• Applicant: Professor Dr.-Ing. Reinhold Kienzler
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 428861960

Functionally graded materials (FGM) are a type of heterogeneous composite materials exhibiting gradual variations in volume fraction of their constituents from one surface of the material to the other, resulting in properties which vary continuously across the material. FGM find their applications, e.g., as dental implants, heat exchange tubes and engine components. Often, they are employed as moderately thick, isotropic and anisotropic plates. Therefore, consistent plate theories should be adopted, which take shear deformations, warping of the cross-section and stress distributions in thickness direction into account. These theories have been developed recently for homogeneous, isotropic and anisotropic materials. Within the research project, they will be extended to treat FGM materials. First of all, a power law and an exponential law of the properties in thickness directions will be considered, later on, also laminated plates with peace-wise constant material properties, which are used most frequently in practical applications. Special emphasis will be placed on the fact that the notion of consistency is changed by the variation of the material properties in thickness direction and must be adjusted in order to meet the requirements of consistency of different orders of approximations.For specific load and boundary conditions, closed-form analytical solutions of the three-dimensional theory of elasticity exist for the bending of functionally graded rectangular plates, which may serve as benchmark for the corresponding plate theories. These are employed to access the quality of the plate theories and to estimate limits of applicability (thickness-to-length ratio, stiffness variations over the thickness).The next step is to develop a finite element (FE) for functionally graded consistent plates and to implement the element into a commercial FE-program package (ABAQUS) as user supplied subroutine. The results of test examples will be compared with three-dimensional FE calculations in order to check the accuracy of the element and its limits of applicability. Further, the results will be compared with those of other plate theories available in the literature in order to check their consistency.The in-plane problem (disc) and the out-of-plane problem (plate) are decoupled only, if the material properties and the loading distribution satisfy certain symmetry conditions. In the last step of the project, unsymmetrical stiffness distributions in thickness direction will be considered, which enjoy a broad potential of application in aero- and astronautics. To this extent, a coupled, consistent disc-plate theory will be developed and compared with existing solutions of the three-dimensional theory of elasticity.

• DFG Programme: Research Grants