Application of theorem of minimum potential energy to a complex structure: Part II: three-dimensional analysis

Abstract

A cylindrical shell with a non-circular cross-section consisting of flat sides and circular arc corners is analyzed using the theorem of minimum potential energy. The three-dimensional analysis builds on previous two-dimensional work. The potential energy expression for the structure is developed, including first-order transverse shear deformation effects. All unknown displacements are represented by power series, and the potential energy expression is rewritten in terms of the summation convention for the power series. The variation of the potential energy expression is taken, leading to a linear system of equations that is solved for the unknown power series coefficients. With the displacements determined, stresses are calculated for a composite sandwich construction. An examination of both short shells (less than twice the boundary layer length) and long shells (more than twice the boundary layer length) is made. The MPE method with power series is found to predict behavior well for short shells, but not for long shells.