Nonlinear Finite Element Analysis

Classification of nonlinearities (geometrical, material and boundary conditions). Strain- and stress measures for large displacements/deformations. Mathematical models for elastic and elastoplastic materials. Geometrical stiffness and linearized buckling. Formulation of the nonlinear finite element method. Numerical integration of dynamically excitated systems. Implicit/explicit time integration. Incremental-iterativ solution methods for nonlinear static and dynamic problems. Modelling of nonlinear boundary conditions. Impact- and contact problems.

Knowledge: The candidate should have knowledge of:

• Description of the nonlinear behavior
• Classification of nonlinearities (geometric, material and boundary conditions)
• Characterization of critical points in the load-displacement diagram
• How to establish and use the total and incremental equilibrium equations
• Incremental-iterative solution methods
• General knowledge of automatic load incrementation and arclength methods
• Material models for elastic and elastic-plastic materials
• Numerical methods for the direct integration of the dynamic equilibrium equations
• Modelling and solution methods for nonlinear boundary conditions (contact)
• Stress and strain measures for the description of large strain
• Basic assumptions of linearized buckling.

Skills: The candidate should be able to:

• Conduct simple nonlinear static and dynamic structural analyses and linearized buckling analysis of simple bar and beam systems by hand calculation methods
• Derive incremental stiffness relation for bar elements based on the expression of potential energy
• Use a general finite element program to model and solve simple nonlinear static and dynamic problems in a qualified manner .

General competence: The candidate should be able to model, choose proper solution technique and perform static and dynamic nonlinear structural analyses of simple structural problems using the finite element method and be able to interpret and assess the accuracy of the computed response.

Digital competence: Skilled use of finite element program (ABAQUS) for nonlinear static and dynamic strength analysis of structures: Modelling, perform the analysis, interpretation of the accuracy and be able to check that the analysis has converged. Programming with Python.

Sustainability competence: The course will teach students to use efficient solution algorithms to optimize structures for material efficiency and strength, and make use of computational strategies that reduce energy consumption in simulations to support sustainable engineering solutions.

Lectures and mandatory exercises. The use of digital tools such as Python and finite element software is emphasized in the exercises.