This course provides a comprehensive introduction to the fundamentals of the Finite Element Method (FEM) and the practical application of User Element (UEL) subroutines in Abaqus. It is designed for students and engineers with no prior experience in FEA or programming. UEL subroutines offer the powerful capability to define custom elements, extending the possibilities beyond built-in element libraries for specialized simulations. This course will bridge the gap from basic theory to hands-on implementation, empowering you to create your own elements to solve unique engineering problems.

Target Audience:

• Engineering students (undergraduate/graduate) new to computational mechanics.
• Industry professionals who use FEA software but want to understand and develop custom functionalities.
• Researchers who need to model novel materials or complex physical phenomena not covered by standard element libraries.

Prerequisites:

• A basic understanding of solid mechanics (stress, strain).
• Familiarity with fundamental calculus and linear algebra concepts.
• Familiarity with ABAQUS/CAE usage.

Learning Objectives: Upon successful completion of this course, students will be able to:

• Explain the core principles and workflow of the Finite Element Method.
• Write, compile, and debug basic Fortran programs.
• Understand the purpose and structure of an ABAQUS UEL subroutine.
• Identify the key variables and arrays used to define an element’s behavior.
• Develop a UEL for a simple structural element (e.g., a truss or beam).
• Set up and run an ABAQUS analysis using a custom user-defined element.

Course Outline

Module 1: Fundamentals of the Finite Element Method (FEM)

• 1.1 What is FEA?
  • Understanding FEM as a numerical technique for solving complex engineering problems.
  • The core idea of discretization: breaking a complex domain into simple pieces.
• 1.2 The FEA Workflow: A High-Level View
  • Preprocessing: Building the model geometry, defining material properties, meshing.
  • Solving: Applying boundary conditions (constraints and loads) and running the numerical solver.
  • Post-processing: Visualizing and interpreting the results (stresses, displacements).
• 1.3 Key Terminology for Beginners
  • Nodes, Elements (1D, 2D, 3D), and Degrees of Freedom (DOF).
  • The Mesh: Creating a network of nodes and elements.
  • Element Stiffness Matrix and the Global Stiffness Matrix.

Module 2: Essential Programming for FEA Subroutines

This module provides the necessary programming skills, focusing on the language most commonly used for Abaqus subroutines.

• 2.1 Introduction to Fortran
  • Why Fortran? Its legacy and efficiency in scientific computing.
  • Setting up a Fortran compiler.
• 2.2 Fortran Programming Basics
  • Program structure, syntax, and data types (integer, real, double precision).
  • Variables and operators.
  • Control structures: IF statements and DO loops.
  • Arrays and matrices: Declaration and manipulation.
  • Writing and calling Subroutines and Functions.

Module 3: Introduction to Abaqus User Subroutines

This module introduces the concept of user subroutines and focuses specifically on the purpose and structure of the UEL.

• 3.1 What is a UEL Subroutine?
  • Its function: Defining the behavior of a user-defined element from scratch.
  • Comparison with other common Abaqus subroutines (e.g., UMAT, which defines material behavior, not the entire element).
• 3.2 The UEL Interface: Anatomy of the Subroutine
  • The subroutine signature and its arguments.
  • Key Input Variables: Nodal coordinates (COORDS), solution-dependent variables (U, DU), element properties (PROPS), etc.
  • Key Output Variables: Right-Hand-Side vector (RHS), stiffness (Jacobian) matrix (AMATRX).
  • State Variables (SVARS) for tracking element history.

Module 4: Developing a basic UEL: Triangular elements for a plane strain structure

This is a hands-on module where we will build a simple, functional UEL from the ground up.

• 4.1 Theoretical Formulation
  • Deriving the element stiffness matrix (AMATRX) and residual vector (RHS).
  • Identifying the necessary inputs (nodal coordinates, material properties) and outputs.
• 4.2 Writing the UEL Fortran Code
  • Step-by-step coding.
  • Assembling the AMATRX and RHS arrays.
• 4.3 Integrating the UEL with ABAQUS
  • The Abaqus input file (.inp): Using the *USER ELEMENT keyword to define the element’s properties (nodes, DOFs, variables).
  • Assigning the user element to a section and a part.
• 4.4 Compiling and Running the Analysis
  • Linking the Fortran source file with the Abaqus solver.
  • The abaqus user= command.
  • Troubleshooting common compilation and runtime errors.
• 4.5 Verifying the Results
  • Checking the UEL results against a known analytical solution or a model built with standard Abaqus elements.

Teaching Methodology:

• Conceptual Lectures: To introduce theoretical FEA and programming concepts.
• Live Coding Demonstrations: Instructor will write and explain the Fortran code in real-time.
• Problem-Based Learning: A final mini-project to solve a simple engineering problem using a custom-developed UEL.

Recommended Resources:

• Primary Text: ABAQUS User Subroutines Reference Manual (specifically the UEL section).
• Supplemental Texts: A standard textbook on introductory Finite Element Analysis.