Thin-walled structures made of foams

Thin-walled structures made of foams, composites, sandwiches or functionally graded materials have many applications in aircraft, automotive, and other industries since they combine functionality, high specific stiffness with light weight. The analysis of such structures can be performed on the base of the three-dimensional theory, but often theories with a lower dimension are applied. The classical plate theory elaborated by Kirchhoff can be applied to thin plates made of classical materials like steel. But this approach is connected with various limitations (e.g., constant material properties in the thickness direction). In addition, mathematical inconsistencies (for example, the order of the governing equation does not correspond to the number of boundary conditions) exist. Many suggestions for improvements of the classical plate theory are made. The engineering direction of improvements was ruled by applications (e.g., the use of laminates or sandwiches as the plate material), and new hypotheses are introduced. In addition, some mathematical approaches like power series expansions or asymptotic integration techniques are applied. A conceptional different direction is the direct approach in the plate theory which is applied to plates made of the above mentioned advanced materials. Within this theory static and the vibration problems are solved assuming linear-elastic and linear-viscoelastic behavior. The material properties are changing in the thickness direction only. It is shown that the results based on the direct approach differ significantly from the classical estimates which can be explained by the non-classical estimation of the transverse shear stiffness. In the last part a general linear six-parametric theory is presented. The kinematics of the plate is described by using the vector of translation and the vector of rotation as the independent variables. The relations between the equilibrium conditions of a three-dimensional micropolar plate-like body and the two-dimensional equilibrium equations of the deformable surface are established.