A kinematically exact rod model for thin-walled members with cross-sectional distortion and finite strains

• Grant number: 22/15644-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2023
• End date: October 31, 2027
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Eduardo de Morais Barreto Campello
• Grantee: Marcos Pires Kassab
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 23/16272-1 - A kinematically exact reduced order model for fracture in thin-walled members, BE.EP.DR

Abstract

In the context of frame structures, kinematically exact rod models are pivotal to correctly capture critical loads and describe post-critical behaviour. Without them, second order analysis may be employed to find critical loads in some usual (though not all) cases, but no post-critical states can be analyzed. For thin-walled members, neglecting local effects can have a significant impact on the stiffness of the cross-section. Moreover, local buckling can be the design limitation in many real-life situations. Currently, two options exist for modelling rods in this context: a) rod models with cross-sectional distortion capabilities (e.g., the Generalized Beam Theory - GBT, models based on the Finite Strip Method - FSM, etc), but with incomplete kinematics (non-exact, usually lacking consistent parametrization of the secondary warping) and linearized constitutive equation (thus not suited for finite strains); and b) kinematically exact shell modes, which are hierarchically superior but computationally more expensive, especially for daily design and analysis. The aim of this work is to develop a fully kinematically exact rod model with consistent cross-sectional distortion and nonlinear elastic (neo-Hookean) constitutive equation, allowing for the accurate evaluation of local buckling as well as the description of configurations with truly large displacements and finite strains. To this aim, distortional modes from the GBT approach will be added to the rigid body motion parametrization of the traditional kinematically exact rod theory. Important adaptations in the theory will be mandatory, in order to treat both the primary (mid-line´s) and secondary (through-the-thickness´) cross sectional distortion and warping. The model will be implemented in a nonlinear finite element program and its outcomes will be validated against reference solutions obtained using hierarchically higher order formulations, having as main reference both shell and 3D solid models. At last, the model´s applicability for the simulation of real engineering applications will be illustrated through a series of representative numerical examples.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

KASSAB, MARCOS PIRES; CAMPELLO, EDUARDO DE MORAIS BARRETO; IBRAHIMBEGOVIC, ADNAN. A DNN-Based Surrogate Constitutive Equation for Geometrically Exact Thin-Walled Rod Members. COMPUTATION, v. 13, n. 3, p. 24-pg., 2025-03-03. (20/13362-1, 22/15644-0, 23/16272-1)

KASSAB, MARCOS PIRES; CAMPELLO, EDUARDO DE MORAIS BARRETO; IBRAHIMBEGOVIC, ADNAN. A geometrically exact thin-walled rod model with warping and stress-resultant-based plasticity obtained with a two-level computational approach. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v. 433, p. 18-pg., 2024-10-30. (22/15644-0, 23/16272-1)