The Finite Element Method for Linear Structural Analysis

About Course

Unlock the power of Finite Element Analysis (FEA) in structural engineering with our comprehensive course, designed to take you from theory to practical proficiency. Over 12 engaging modules, you’ll delve deep into the intricacies of FEA and reinforce your knowledge through hands-on workshops (exercises on FEA software). Whether you’re a novice looking to start your journey or a seasoned professional seeking to refine your skills, this course has something valuable to offer at every level.

Module 1: Introduction to Finite Element Analysis

– Fundamental Concepts

– Why is FEM so important?

– Workshop 01: Building Your First Finite Element Model: Bike Crank

Module 2: Linear Elastic Spring Element

– Spring theory

– System Assembly in Global Coordinates

– Exercises

– Workshop 02: Linear Spring Element

Module 3: Elastic Bar Element

– Bar theory

– Exercise

– Strain Energy

– Castigliano’s First Theorem

– Minimum Potential Energy

– Workshop 03: Linear Bar Element

Module 4: Truss Structures

– Nodal Equilibrium Equations

– Element Transformation

– Direct Assembly of Global Stiffness Matrix

– Boundary Conditions, Constraint Forces

– Element Strain and Stress

– Comprehensive Example

– Three dimensional Trusses

– Workshop 04: 2D Truss Structure

Module 5: Beam Element

– Elementary Beam Theory

– Beam Element

– Beam Element Stiffness Matrix

– Element Load Vector

– Work Equivalence for Distributed Loads

– Flexure Element with Axial Loading

– A General Three-Dimensional Beam Element

– Workshop 05: Beam Element

Module 6: Equations of Elasticity

– Strain-Displacement Relations

– Stress-Strain Relations

– Equilibrium Equations

– Summary

Module 7: Matrix Mathematics and Solution Techniques for Linear Algebraic Equations

– Matrix Mathematics

– Solution Techniques for Linear Algebraic Equations

Module 8: Plane Stress

– Equations of Elasticity for Plane Stress

– Finite Element Formulation: Constant Strain Triangle

– Stiffness Matrix Evaluation

– Distributed Loads

– Body Forces

– Workshop 06: Rectangular Plate with Central Circular Hole

Module 9: Plane Strain

– Equations of Elasticity for Plane Strain

– Finite Element Formulation: Four-node Rectangle

– Numerical Integration: Gaussian Quadrature

– Workshop 07: C-Clamp

Module 10: Isoparametric Formulation

– Four-node quadrilateral element

– Exercise

– Singularity of the Jacobian Matrix

Module 11: General Three-Dimensional Stress Elements

– Introduction

– Equations of Elasticity

– Finite Element Formulation

– Example: 4-node Tetrahedral

– Stress and Strain Computation

– Workshop 08: Connecting Lug

Module 12: Shell Elements

– Plate Element Theory

– Plate Element Formulation

– Shell Element Theory

– Workshop 10: Thin Folded Plate

Throughout this course, you’ll receive expert guidance, learn best practices, and gain practical experience to tackle real-world structural analysis challenges confidently. Don’t miss this opportunity to become a proficient Finite Element Analysis practitioner and enhance your career in structural engineering. Join us today and embark on a journey toward mastering FEA.

Formulation of key types of finite elements, including spring, bar, beam, plane stress and strain, 3D, and shell elements.
In-depth finite element theory presented in a simple, easy-to-understand way.
Hands-on practice with FEA software, where each exercise is directly connected to the theory covered.
Complete FEA structure, covering pre-analysis, model setup, verification, validation, and post-processing.

Course Content

Introduction

Course Material
Introduction – Part 1

13:27
Introduction – Part 2

11:32
Introduction – Part 3

14:47
Abaqus Instalation Guide

15:49
Workshop 01 – Connecting Lug – Problem Specification

12:35
Workshop 01 – Connecting Lug – Pre-analysis

13:10
Workshop 01 – Connecting Lug – Create Domain

18:03
Workshop 01 – Connecting Lug – Mesh the Domain

21:09
Workshop 01 – Connecting Lug – Create Material and Instance

10:33
Workshop 01 – Connecting Lug – Apply BCs and Solve BVP

13:42
Workshop 01 – Connecting Lug – Verification – Part 1

19:32
Workshop 01 – Connecting Lug – Verification – Part 2

14:50
Workshop 01 – Connecting Lug – Verification – Part 3

18:01
Workshop 01 – Connecting Lug – Convergence Study

10:53

Linear Elastic Spring Element

Linear Elastic Spring Element – Part 1

16:21
Linear Elastic Spring Element – Part 2

20:59
Linear Elastic Spring Element – Part 3

19:32
System Assembly in Global Coordinates – Part 1

16:05
System Assembly in Global Coordinates – Part 2

27:15
Exercises – Part 1

28:57
Exercises – Part 2

29:51
Workshop 02 – Spring Element – Pre-analysis

16:20
Workshop 02 – Spring Element – Define Domain

14:01
Workshop 02 – Spring Element – Define BCs and Governing Equations

20:44
Workshop 02 – Spring Element – Verification

14:05
Workshop 02 – Spring Element – Study Input File

14:10

Linear Elastic Bar Element

Elastic Bar Element – Part 1

10:21
Elastic Bar Element – Part 2

15:26
Elastic Bar Element – Part 3

20:51
Exercise – Part 1

13:59
Exercise – Part 2

11:59
Exercise – Part 3

09:23
Strain Energy

20:31
Castigliano’s First Theorem – Part 1

20:07
Castigliano’s First Theorem – Part 2

28:41
Minimum Potential Energy – Part 1

20:12
Minimum Potential Energy – Part 2

13:52
Workshop 03 – Bar Element – Problem Specification

05:48
Workshop 03 – Bar Element – Pre-Analysis

21:29
Workshop 03 – Bar Element – Define Domain

13:25
Workshop 03 – Bar Element – Setup BCs and Define Governing Equation

18:10
Workshop 03 – Bar Element – Post-Processing

16:55
Workshop 03 – Bar Element – Analyse input file

21:17

Truss Structures

Nodal Equilibrium Equations – Part 1

27:11
Nodal Equilibrium Equations – Part 2

28:48
Element Transformation

30:18
Direct Assembly of Global Stiffness Matrix – Part 1

17:04
Direct Assembly of Global Stiffness Matrix – Part 2

28:53
Direct Assembly of Global Stiffness Matrix – Part 3

17:06
Boundary Conditions, Constraint Forces

18:16
Element Strain and Stress – Part 1

22:35
Element Strain and Stress – Part 2

38:12
Comprehensive Example – Part 1

30:07
Comprehensive Example – Part 2

33:38
Comprehensive Example – Part 3

53:33
Three dimensional Trusses – Part 1

21:56
Three dimensional Trusses – Part 2

22:23
Workshop 04 – Problem Specification

08:23
Workshop 04 – Pre-analysis

16:56
Workshop 04 – Define BPV – Part 1

17:41
Workshop 04 – Define BPV – Part 2

14:16
Workshop 04 – Verification

23:52
Workshop 04 – Input File

13:07

Beam Element

Elementary Beam Theory – Part 1

21:59
Elementary Beam Theory – Part 2

20:12
Elementary Beam Theory – Part 3

33:28
Beam Element

29:28
Beam Element Stiffness Matrix – Part 1

26:34
Beam Element Stiffness Matrix – Part 2

25:49
Element Load Vector and Exercise

30:04
Work Equivalence for Distributed Loads – Part 1

22:38
Work Equivalence for Distributed Loads – Part 2

18:14
Flexure Element with Axial Loading – Part 1

25:11
Flexure Element with Axial Loading – Part 2

20:34
Flexure Element with Axial Loading – Part 3

21:19
A General Three-Dimensional Beam Element – Part 1

17:44
A General Three-Dimensional Beam Element – Part 2

13:30
Workshop 05 – Problem Specification

11:08
Workshop 05 – Pre-analysis

15:42
Workshop 05 – BPV Definition – Part 1

20:27
Workshop 05 – BPV Definition – Part 2

29:38
Workshop 05 – BPV Definition – Part 3

19:08
Workshop 05 – Verification

25:12
Workshop 05 – Analyse Stress and Displacement

19:59

Equations of Elasticity

Matrix Mathematics and Solution Techniques for Linear Algebraic Equations

Plane Stress

Equations of Elasticity for Plane Stress

30:58
Finite Element Formulation Constant Strain Triangle – Part 1

41:29
Finite Element Formulation Constant Strain Triangle – Part 2

29:52
Finite Element Formulation Constant Strain Triangle – Part 3

34:50
Summary and Stiffness Matrix Evaluation

27:07
Distributed Loads – Part 1

41:22
Distributed Loads – Part 2

38:36
Body Forces – Part 1

23:52
Body Forces – Part 2

24:09
Workshop 06 – Pre-analysis

27:54
Workshop 06 – BVP Definition – Part 1

23:42
Workshop 06 – BVP Definition – Part 2

32:37
Workshop 06 – Symmetry Condition

27:58
Workshop 06 – Convergence Study

41:29
Workshop 06 – End of Verification

30:50
Workshop 06 – Final Comments

27:15

Plane Strain

Equations of Elasticity for Plane Strain

23:39
Finite Element Formulation Four-node Rectangle – Part 1

27:21
Finite Element Formulation Four-node Rectangle – Part 2

36:02
Finite Element Formulation Four-node Rectangle – Part 3

28:42
Finite Element Formulation Four-node Rectangle – Part 4

24:08
Numerical Integration Gaussian Quadrature – Part 1

22:36
Numerical Integration Gaussian Quadrature – Part 2

33:11
Workshop 07 – Pre-Analysis

24:54
Workshop 07 – Define BVP

27:49
Workshop 07 – Shear Locking

56:36
Workshop 07 – Hourglass and Incompatible mode elements

25:42
Workshop 07 – Numerical Singularity

26:11

Isoparametric Formulation

General Three Dimensional Stress Element

Introduction and Equations of Elasticity

26:52
Finite Element Formulation

27:20
Example: 4-node Tetrahedral

33:54
Stress and Strain Computation – Stress vs Strain Curve

29:01
Stress and Strain Computation – Maximum shear stress theory

33:58
Stress and Strain Computation – Distortion Energy Theory

23:22
Workshop 09 – Pre-analysis

08:16
Workshop 09 – Define BVP – Part 1

29:51
Workshop 09 – Define BVP – Part 2

28:28
Workshop 09 – Post-Processing

29:35

Shell Element

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About Course

What Will You Learn?

Course Content

Introduction

Course Material

Introduction – Part 1

Introduction – Part 2

Introduction – Part 3

Abaqus Instalation Guide

Workshop 01 – Connecting Lug – Problem Specification

Workshop 01 – Connecting Lug – Pre-analysis

Workshop 01 – Connecting Lug – Create Domain

Workshop 01 – Connecting Lug – Mesh the Domain

Workshop 01 – Connecting Lug – Create Material and Instance

Workshop 01 – Connecting Lug – Apply BCs and Solve BVP

Workshop 01 – Connecting Lug – Verification – Part 1

Workshop 01 – Connecting Lug – Verification – Part 2

Workshop 01 – Connecting Lug – Verification – Part 3

Workshop 01 – Connecting Lug – Convergence Study

Linear Elastic Spring Element

Linear Elastic Spring Element – Part 1

Linear Elastic Spring Element – Part 2

Linear Elastic Spring Element – Part 3

System Assembly in Global Coordinates – Part 1

System Assembly in Global Coordinates – Part 2

Exercises – Part 1

Exercises – Part 2

Workshop 02 – Spring Element – Pre-analysis

Workshop 02 – Spring Element – Define Domain

Workshop 02 – Spring Element – Define BCs and Governing Equations

Workshop 02 – Spring Element – Verification

Workshop 02 – Spring Element – Study Input File

Linear Elastic Bar Element

Elastic Bar Element – Part 1

Elastic Bar Element – Part 2

Elastic Bar Element – Part 3

Exercise – Part 1

Exercise – Part 2

Exercise – Part 3

Strain Energy

Castigliano’s First Theorem – Part 1

Castigliano’s First Theorem – Part 2

Minimum Potential Energy – Part 1

Minimum Potential Energy – Part 2

Workshop 03 – Bar Element – Problem Specification

Workshop 03 – Bar Element – Pre-Analysis

Workshop 03 – Bar Element – Define Domain

Workshop 03 – Bar Element – Setup BCs and Define Governing Equation

Workshop 03 – Bar Element – Post-Processing

Workshop 03 – Bar Element – Analyse input file

Truss Structures

Nodal Equilibrium Equations – Part 1

Nodal Equilibrium Equations – Part 2

Element Transformation

Direct Assembly of Global Stiffness Matrix – Part 1

Direct Assembly of Global Stiffness Matrix – Part 2

Direct Assembly of Global Stiffness Matrix – Part 3

Boundary Conditions, Constraint Forces

Element Strain and Stress – Part 1

Element Strain and Stress – Part 2

Comprehensive Example – Part 1

Comprehensive Example – Part 2

Comprehensive Example – Part 3

Three dimensional Trusses – Part 1

Three dimensional Trusses – Part 2

Workshop 04 – Problem Specification

Workshop 04 – Pre-analysis

Workshop 04 – Define BPV – Part 1

Workshop 04 – Define BPV – Part 2

Workshop 04 – Verification

Workshop 04 – Input File

Beam Element

Elementary Beam Theory – Part 1

Elementary Beam Theory – Part 2

Elementary Beam Theory – Part 3

Beam Element

Beam Element Stiffness Matrix – Part 1

Beam Element Stiffness Matrix – Part 2

Element Load Vector and Exercise

Work Equivalence for Distributed Loads – Part 1