Evaluation of Variable Kinematics Beam, Plate, and Shell Theories using the Asymptotic-Axiomatic Method

This paper proposes a novel approach to evaluate structural theories based on their accuracy and computational efficiency. The focus is on beam, plate, and shell theories built using polynomial expansions of the displacement field. The structural theories and related finite element matrices are obtained through the Carrera Unified Formulation. Each displacement component can have different expansions, and the choice of the generalized variables to include is an input for the analysis. Similar results were obtained in previous works through penalization techniques applied to the finite element matrices. This paper presents a novel approach to building finite element matrices based on truncated expansions of the unknown variables, leading to smaller matrices and lower computational costs. Best theories concerning accuracy and computational costs are retrieved and presented through Best Theory Diagrams. Numerical results consider verification with data from literature and the analysis of structural problems with localized effects, such as pinched shells and end-effect problems. The results show the importance of correctly choosing the generalized variables, which may lead to reduced computational costs with negligible accuracy loss.