Influence of a shearing force on optimal design of shells against buckling under overall bending

Optimal design of shells against buckling under overall bending and external pressure

“…For pure bending case of loading (n 0 Z0, m b0 Z0, m b1 Z1) the optimal structure is a cylindrical shell (the first rows in Tables 2 and 4 -r(0)Zr(1)Z1) with the variable wall-thickness, whereas accounting for a shearing effect (n 0 Z0, m b0 Z1, m b1 Z0) leads to the optimal shell with double curvature (the first rows in Tables 1 and 3), where the geometrical constraint is active, r(1)Zr adm Z0.5. These results are in agreement with [3,5]. On the other hand, a limit case of a pure external pressure (n 0 /N) leads to an optimal shell, which is fully axial symmetric double curvature structure (wall thickness is also axially symmetric).…”

“…It allows satisfying the conditions of continuity of the function up to the second derivative. This procedure was applied in [3][4][5] to optimization of shells under stability constraints. It turned out that more effective and even easier in application is introducing the Bézier polynomial (only one but of enough high order), which approximates a shape of the whole shell.…”

“…This same concept was applied in the papers by Krużelecki et al [23] and Ż yczkowski et al [42] devoted to optimal design of axially symmetrical shell under thermal loadings. A combined axial compression and twisting is considered by Barski et al [6], axial compression, bending and twisting by Barski and Krużelecki [3], bending with shearing force taken into account by Barski and Krużelecki [4,5].…”

“…In the papers mentioned above, devoted to optimization of shells with a double curvature, the optimized structures were loaded either by surface loading [20][21][22] or by generalized forces [3][4][5] acting mainly at the edges of shells.…”

An optimal design model for the wall thickness of the propellant tank

“…16 Barski et al considered the stability of the shell with a double positive curvature and studied the optimal design of the shell shape and thickness against bucking subjected to the bending moment, the shearing force, the axial force, and torsional moment. [17][18][19][20] Nonetheless, there is a lack of an efficient optimal design model for the wall thickness. In this paper, an optimal design model for the wall thickness of the propellant tank is proposed to decrease the mass and optimize the stress distribution of the tank.…”