The Finite Element Method for Nonlinear Structural Analysis

This advanced course is intended for engineers and researchers who already have a solid understanding of linear Finite Element Analysis (FEA). It is recommended that participants complete the prerequisite course, The Finite Element Method for Linear Structural Analysis developed by LearnFEA, or possess equivalent knowledge of linear FEA concepts and applications.

The training combines theoretical depth with hands-on projects, enabling you to confidently analyze complex nonlinear phenomena using Abaqus and BETA CAE tools (ANSA & META). Structured into six in-depth modules, the course explores the full spectrum of nonlinearities—material, geometric, and contact—while progressively building up to the general formulation of nonlinear FEA using modern tensor notation and variational principles.

Course Modules

Module 1: Introduction

We begin with a high-level overview of the main types of nonlinearities: material, large displacements, large deformations, and contact. Though not yet focusing on the full mathematical formulation, this module sets the stage with conceptual insights and introductory simulations in Abaqus. It closes with the first discussion on stiffness matrix updating in nonlinear analysis.

Module 2: Solution of Simple Nonlinear Problems

This module isolates each nonlinearity through simplified problems that are first solved by hand and then verified in Abaqus. It includes material nonlinearity (plasticity), geometric nonlinearity (large displacements and structural instability), and basic contact modeling (GAP element). The objective is to build intuition and reinforce understanding before moving to the general nonlinear formulation.

Module 3: Geometric Nonlinearity – Understanding the Concept from One-Dimensional
Focusing on large displacements and deformations, this module explores geometric nonlinearity using a one-dimensional beam model. The coupling between axial and bending effects is addressed through the Geometric Stiffness Matrix, derived via the Principle of Virtual Work. We extend these insights to shell elements. We also apply the geometric stiffness matrix to classical linear buckling problems. The module concludes with a deeper look at large deformations.

Module 4: General Formulation of Nonlinear FEM
This core module introduces the full mathematical framework for nonlinear FEA. We begin with a study of stress transformations in one, two, and three dimensions, followed by an introduction to tensors and indicial notation. We then explore the deformation gradient tensor, a central concept in finite strain theory, and its polar decomposition into rotation and stretch components. These concepts provide the foundation for defining various strain and stress measures, such as the Green-Lagrange strain, Almansi strain, Cauchy stress, and the first and second Piola-Kirchhoff stress tensors. The module culminates with the variational formulation of the nonlinear finite element method using the Principle of Virtual Work.

Module 5: Advanced Plasticity Modeling
A detailed study of plastic behavior in materials is presented, including yield criteria (e.g., von Mises), flow rules (such as the Prandtl-Reuss equations), and advanced hardening laws (isotropic, kinematic, and distortional). The focus is on integrating these models into nonlinear FEA and understanding their impact on structural response under complex loading.

Module 6, 7, 8 … : Complex FEA Problems with ANSA, Abaqus, and META
The final modules emphasizes real-world applications. Participants will learn to handle complex preprocessing tasks in ANSA, solve models in Abaqus, and postprocess results using META. The problems are inspired by research papers and industrial case studies, reflecting the complexity of practical nonlinear simulations. Complete training on ANSA and META is provided to ensure participants are fully equipped to use these tools.

By the end of this course, you will be equipped to formulate, model, and solve nonlinear structural problems with both theoretical rigor and practical confidence. Whether your focus is academic research or industrial design, this course will elevate your nonlinear FEA capabilities to a professional level.