Buckling mechanism of thin-walled arches with composite polyhedral shapes

Abstract

The present work is concerned with the pressure capacity of the thin-walled composite arches with different polyhedral shapes. The analytical derivation process involves the employment of the energy theory, the thin-walled shell principle, and the assumed displacement field. The total potential energy formulae of the polyhedral arch are expressed analytically. By taking the first derivatives of the energy function to the two unknowns, it is effortless to obtain two equations of equilibrium. The critical buckling pressure and the equilibrium paths are expressed by solving these two equations of equilibrium simultaneously. Subsequently, good agreements are reached when the proposed buckling pressure is compared with other closed-form expressions for a circular arch with a constant radius. Finally, the effect of the geometric parameters on the critical buckling pressure is analyzed. An enhancement factor is introduced to express the ratio of the buckling pressure between the arch with the polyhedral shapes and the traditional circular cross-section. It is found the enhancement factor reduces when the values of N increases and the ratio of thickness-to-radius increases, respectively. Therefore, a polyhedral arch with a small value of N and a small ratio of thickness-to-radius is recommended in engineering applications.