Axisymmetric accurate nonlinear analytical solutions for circular thin membranes under various transverse distributed loads

Abstract

Membrane structures, prized for their light weight and adaptability, are widely used in fields such as engineering, architecture, and aerospace. Nonlinear membrane analysis has evolved from the early works by Föppl and Hencky to modern computational methods. This paper extends the innovative orthogonal power function series, initially developed for circular thin plates, to solve general membrane problems. By expanding deflection using the innovative orthogonal power series and applying the Airy stress function, the method accounts for nonlinear interactions between deflection and in-plane forces. The energy variational method is used to derive nonlinear algebraic equations, enhancing both accuracy and computational efficiency compared to traditional methods. This approach sets new benchmarks for the verification of nonlinear solutions, making it a reliable and practical tool for membrane theory and engineering applications.