Application of theorem of minimum potential energy to a complex structure Part I: two-dimensional analysis

A non-circular shell cross-section with flat sides and circular arc corners is analyzed using the theorem of minimum potential energy. Two-dimensional, plane strain assumptions are utilized, and the potential energy (PE) expression for the structure is developed, including first-order transverse shear deformation effects. The unknown displacements are represented by power series, and the PE expression is rewritten in terms of the summation convention for the power series. The variation of the PE 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. Excellent agreement is found with other analytical methods and with finite element analyses.