The Finite Element Method for Nonlinear Structural Analysis

Advanced Theory and Applications of Material, Geometric, and Contact Nonlinearities in Structural FEA
What you'll learn
Master the fundamentals of nonlinear FEA, including material, geometric, and contact nonlinearities.
Learn to solve complex nonlinear problems, from material plasticity to large deformations.
Acquire the skills to model and analyze advanced plasticity behaviors, including yield criteria and flow rules.
Explore real-world applications through case studies and research-inspired problems.
Understand and apply the full mathematical framework for nonlinear FEA, including deformation gradient tensors and stress-strain measures.
Build confidence in formulating and solving nonlinear structural problems for both academic and industrial applications.
Gain hands-on experience with advanced FEA tools such as Abaqus, ANSA, and META.
Develop a deep understanding of stress transformations, tensors, and variational principles.
Build intuition by solving nonlinear problems in Abaqus.
Learn to apply the Geometric Stiffness Matrix to solve nonlinear buckling and large deformation problems.
Enhance your ability to perform complex preprocessing tasks and post-processing with ANSA and META tools.
Requirements
Prerequisite Knowledge: A solid understanding of linear Finite Element Analysis (FEA) is required. Completion of "The Finite Element Method for Linear Structural Analysis" course by LearnFEA is recommended.
Mathematical Foundation: A basic understanding of linear algebra, calculus, and mechanics of materials is beneficial for understanding advanced concepts.
Commitment: This is an advanced course, so participants should be prepared for in-depth theoretical discussions as well as practical problem-solving.
Hands-On Projects: Active participation in solving real-world FEA problems is required to maximize learning. Completion of all course modules and exercises is encouraged.
Description
The Finite Element Method for Nonlinear Structural Analysis (Introductory Version)This course is a partial version of the complete training The Finite Element Method for Nonlinear Structural Analysis.It is designed for engineers and researchers who already have a solid understanding of linear Finite Element Analysis (FEA). Participants are encouraged to complete the prerequisite course The Finite Element Method for Linear Structural Analysis or have 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 nine comprehensive modules, the full course explores the entire range of nonlinearities-material, geometric, and contact-while progressively developing the general formulation of nonlinear FEA using tensor notation and variational principles.Modules Included in This Udemy Course:Module 1: IntroductionWe 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 ProblemsThis 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 6: Simulation of Bolted End-Plate ConnectionA complete FEA tutorial covering every stage of the analysis - from geometry creation and meshing to the definition of contact interactions, bolt pretension, boundary conditions, load applications and much more. The study is based on a scientific article that provides experimental data of the physical test, allowing direct validation of the numerical model.Workflow: Pre-processing in ANSA, solving in Abaqus Standard, and post-processing in META Post.Modules Available Only in the Full Course (not available here on Udemy):Module 3: Geometric Nonlinearity - Understanding the Concept from One-DimensionalFocusing 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 FEAThis 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 ModelingA 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 7: CrossKart Tutorial - Rear Suspension FEA ModelingComprehensive FEA modeling of the rear suspension of a CrossKart vehicle using advanced techniques commonly applied in the automotive industry. The tutorial covers mesh generation, bolt pretension setup using translator connectors, surface-to-surface and tie contact definitions, multiple connector types, rigid body definitions, step setup, weld modeling and much more.Workflow: Pre-processing in ANSA, solving in Abaqus Standard, and post-processing in META Post.Module 8: CrossKart Tutorial - Front Suspension FEA ModelingA continuation of the previous tutorial, focusing on the front suspension of the same CrossKart vehicle. The same workflow and methodology are applied to ensure consistency and integration with the rear suspension model.Workflow: Pre-processing in ANSA, solving in Abaqus Standard, and post-processing in META Post.Module 9: CrossKart Tutorial - Full Vehicle FEA ModelingIn this module, the front and rear suspension models developed in the previous tutorials are combined, and the remaining vehicle components are modeled to create a complete full-vehicle assembly. This model can be used for various durability and performance analyses, including structural strength, joint integrity, buckling, and explicit dynamic simulations for impact events.Workflow: Pre-processing in ANSA, solving in Abaqus Standard, and post-processing in META Post.By the End of This Udemy Course:You will have a solid conceptual and practical foundation to begin working with nonlinear FEA in Abaqus, including:Understanding the different types of nonlinearities.Solving simple nonlinear problems by hand and in Abaqus.Executing a complete real-world simulation of a bolted end-plate connection, validated with experimental data.
Who this course is for
Engineers with a background in linear Finite Element Analysis (FEA) looking to advance their skills.\nResearchers and academics in the fields of structural mechanics and computational engineering.\nProfessionals in industries such as automotive, aerospace, and manufacturing involved in nonlinear structural analysis.\nAdvanced students or graduates seeking to specialize in nonlinear FEA for research or industry applications.\nFEA practitioners who want to deepen their understanding of complex material, geometric, and contact nonlinearities.
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