Analysis of stochastically parameterized prestressed beams and frames. (15th December 2021) - Larsen, Mikkel Løvenskjold; Adhikari, Sondipon; Arora, Vikas
Abstract: The stochastic behaviour of materials and loading is of great importance for buckling and analysis of prestressed beam and frame structures. In this paper, the stochastic stiffness and stress stiffness matrices are developed for stochastic analysis and buckling analysis. The bending rigidity and the buckling load are modelled as stochastic fields. The spectral decomposition known as the Karhunen–Loéve expansion has been used to expand the random fields. Using the Karhunen–Loéve expansion, the stiffness and stress stiffness closed-form matrices are formulated in terms of discrete parameters. The matrices are developed considering both classical Euler–Bernoulli theory and Timoshenko beam theory. Two case studies involving a pinned-pinned column and a frame structure is used to demonstrate the effectiveness of the proposed methods. Highlights: Karhunen–Loéve expansion is used to develop the closed-form stochastic matrices. Stochastic matrices considers both Euler–Bernoulli and Timoshenko beam theories. The developed matrices will allow for efficient and fast computation. Two numerical case studies are presented to predict the stochastic responses.