(Solved): Two cubes made of soft linear-elastic materials are placed in a cavity of a steel box (as shown in ...

Two cubes made of soft linear-elastic materials are placed in a cavity
of a steel box (as shown in the figure below). The Young's moduli and
Poisson's ratios of the materials are E1 and E2 and ?1 and ?2 ,
respectively. The initial size of the cubes is a × a × a and there are no
gaps between the cubes and the cavity. A force P applied through a
steel plate loads the top surface of the cubes. The box and plate can be
considered as rigid compared with the cube materials. The friction on
all interfaces is negligible. Determine:
a) The stress state in the cube materials; [20 marks]
b) The displacement of the rigid plate, ????, in terms of the cube material
properties, sizes, and the applied force, P. [10 marks]
Do calculations for E1 = 200 GPa; E2 = 70 GPa; ?1 = ?2 = 0.3; ???? = 100 mm and P = 100 kN.???????