The Finite Element Method (Fem/Fea)

From Novice to Pro: FEA Proficiency Unleashed

What you'll learn

Uncover the theory underpinning finite element method and gain hands-on experience with commercial software, demystifying its inner workings.

Learn the foundations of finite element analysis and unlock the secrets behind commercial software, making it a transparent tool in your engineering arsenal.

Bridge the gap between theory and practice as you navigate the finite element method, enhancing your ability to decipher the mechanics of commercial software.

Equip yourself with a deep understanding of finite element theory and practical software proficiency, ensuring you're not limited by 'black box' solutions.

Requirements

Basic Engineering Knowledge: Students should have a fundamental understanding of engineering principles, including mathematics, physics, and mechanics.

A Willingness to Learn: An eagerness to dive deep into the theoretical concepts and commit to hands-on practice is crucial for success in this course.

Description

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 11 engaging modules, you'll delve deep into the intricacies of FEA and reinforce your knowledge through hands-on workshops. 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 CrankModule 2: Linear Elastic Spring Element- Spring theory- System Assembly in Global Coordinates- Exercises- Workshop 02:  Linear Spring ElementModule 3: Elastic Bar Element- Bar theory- Exercise- Strain Energy- Castigliano’s First Theorem- Minimum Potential Energy- Workshop 03: Linear Bar ElementModule 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 StructureModule 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 ElementModule 6: Equations of Elasticity- Strain-Displacement Relations- Stress-Strain Relations- Equilibrium Equations- SummaryModule 7: Matrix Mathematics and Solution Techniques for Linear Algebraic Equations- Matrix Mathematics- Solution Techniques for Linear Algebraic EquationsModule 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 HoleModule 9: Plane Strain- Equations of Elasticity for Plane Strain- Finite Element Formulation: Four-node Rectangle- Numerical Integration: Gaussian Quadrature- Workshop 07: C-ClampModule 10: Isoparametric Formulation- Four-node quadrilateral element- Exercise- Singularity of the Jacobian MatrixModule 11: General Three-Dimensional Stress Elements- Introduction- Equations of Elasticity- Finite Element Formulation- Example: 4-node Tetrahedral- Stress and Strain Computation- Workshop 08: Connecting LugThroughout 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.

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 Software Installation Guide

Lecture 3 Workshop 01 - Pre-analysis

Lecture 4 Workshop 01 - Bike Crank - Define Material and Save the Project

Lecture 5 Workshop 01 - Bike Crank - Geometry

Lecture 6 Workshop 01 - Bike Crank - Setup, Solution and Post-Processing

Lecture 7 Workshop 01 - Bike Crank - Verification, Part 1

Lecture 8 Workshop 01 - Bike Crank - Verification, Part 2

Section 2: Linear Elastic Spring Element

Lecture 9 Linear Elastic Spring Element

Lecture 10 System Assembly in Global Coordinates

Lecture 11 Exercises - Part 1

Lecture 12 Exercises - Part 2

Lecture 13 Workshop 02 - Problem Specification and Pre-analysis

Lecture 14 Workshop 02 - Material and Geometry

Lecture 15 Workshop 02 - Creating the Springs and Mesh

Lecture 16 Workshop 02 - Applying BCs, Solving the Model and Post-processing

Lecture 17 Workshop 02 - Verification

Lecture 18 Workshop 02 - ANSYS Help

Section 3: Elastic Bar Element

Lecture 19 Elastic Bar Element

Lecture 20 Exercise

Lecture 21 Strain Energy

Lecture 22 Castigliano's First Theorem

Lecture 23 Minimum Potential Energy

Lecture 24 Workshop 03 - Problem Specification and Pre-analysis

Lecture 25 Workshop 03 - Creating Material

Lecture 26 Workshop 03 - Creating the Geometry

Lecture 27 Workshop 03 - Analysis Setup on Mechanical

Lecture 28 Workshop 03 - Post-processing results

Lecture 29 Workshop 03 - Verification

Section 4: Truss Structures

Lecture 30 Nodal Equilibrium Equations - Part 1

Lecture 31 Nodal Equilibrium Equations - Part 2

Lecture 32 Nodal Equilibrium Equations - Part 3

Lecture 33 Element Transformation

Lecture 34 Direct Assembly of Stiffness Matrix - Part 1

Lecture 35 Direct Assembly of Stiffness Matrix - Part 2

Lecture 36 Direct Assembly of Stiffness Matrix - Part 3

Lecture 37 Boundary Conditions, Constraint Forces

Lecture 38 Element Strain and Stress - Part 1

Lecture 39 Element Strain and Stress - Part 2

Lecture 40 Comprehensive Example - Part 1

Lecture 41 Comprehensive Example - Part 2

Lecture 42 Comprehensive Example - Part 3

Lecture 43 Three dimensional Trusses - Part 1

Lecture 44 Three dimensional Trusses - Part 2

Lecture 45 Workshop 04 - Problem Specification and Pre-analysis

Lecture 46 Workshop 04 - Solving using Excel

Lecture 47 Workshop 04 - Creating Geometry

Lecture 48 Workshop 04 - Define Material and Create Mesh

Lecture 49 Workshop 04 - Apply Boundary Conditions and Solve the Model

Lecture 50 Workshop 04 - Post-processing

Lecture 51 Workshop 04 - Verification

Section 5: Beam Element

Lecture 52 Elementary Beam Theory - Part 1

Lecture 53 Elementary Beam Theory - Part 2

Lecture 54 Elementary Beam Theory - Part 3

Lecture 55 Beam Element

Lecture 56 Beam Element Stiffness Matrix - Part 1

Lecture 57 Beam Element Stiffness Matrix - Part 2

Lecture 58 Beam Element Stiffness Matrix - Part 3

Lecture 59 Element Load Vector and Exercise - Part 1

Lecture 60 Element Load Vector and Exercise - Part 2

Lecture 61 Element Load Vector and Exercise - Part 3

Lecture 62 Work Equivalence for Distributed Loads - Part 1

Lecture 63 Work Equivalence for Distributed Loads - Part 2

Lecture 64 Work Equivalence for Distributed Loads - Part 3

Lecture 65 Flexure Element with Axial Loading - Part 1

Lecture 66 Flexure Element with Axial Loading - Part 2

Lecture 67 Flexure Element with Axial Loading - Part 3

Lecture 68 A General Three Dimensional Beam Element - Part 1

Lecture 69 A General Three Dimensional Beam Element - Part 2

Lecture 70 Simple Beam Element Example on FEA Software

Lecture 71 Workshop 05 - Problem Specification

Lecture 72 Workshop 05 - Pre-analysis

Lecture 73 Workshop 05 - Define Material

Lecture 74 Workshop 05 - Define Geometry

Lecture 75 Workshop 05 - Generate Mesh

Lecture 76 Workshop 05 - Define Boundary Conditions and Solve

Lecture 77 Workshop 05 - Post-processing, Part 1

Lecture 78 Workshop 05 - Post-processing, Part 2

Lecture 79 Workshop 05 - Post-processing, Part 3

Lecture 80 Workshop 05 - Verification

Section 6: Equations of Elasticity

Lecture 81 Strain-Displacement Relations, Part 1

Lecture 82 Strain-Displacement Relations, Part 2

Lecture 83 Stress-Strain Relations

Lecture 84 Equilibrium Equations, Part 1

Lecture 85 Equilibrium Equations, Part 2

Lecture 86 Equilibrium Equations, Part 3

Lecture 87 Summary

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

Lecture 88 Matrix Mathematics - Part 1

Lecture 89 Matrix Mathametics - Part 2

Lecture 90 Matrix Mathematics - Part 3

Lecture 91 Solution Techniques for Linear Algebraic Equations - Part 1

Lecture 92 Solution Techniques for Linear Algebraic Equations - Part 2

Lecture 93 Solution Techniques for Linear Algebraic Equations - Part 3

Section 8: Plane Stress

Lecture 94 Equations of Elasticity for Plane Stress Part 1

Lecture 95 Equations of Elasticity for Plane Stress Part 2

Lecture 96 Equations of Elasticity for Plane Stress Part 3

Lecture 97 Finite Element Formulation - Constant Strain Triangle - Part 1

Lecture 98 Finite Element Formulation - Constant Strain Triangle - Part 2

Lecture 99 Finite Element Formulation - Constant Strain Triangle - Part 3

Lecture 100 Stiffness Matrix Evaluation

Lecture 101 Distributed Loads - Part 1

Lecture 102 Distributed Loads - Part 2

Lecture 103 Body Forces - Part 1

Lecture 104 Body Forces - Part 2

Lecture 105 Beam Example - Part 1

Lecture 106 Beam Example - Part 2

Lecture 107 Beam Example - Part 3

Lecture 108 Beam Example - Part 4

Lecture 109 Workshop 06 - Problem Specification and Pre-analysis

Lecture 110 Workshop 06 - Define Material and Geometry

Lecture 111 Workshop 06 - First configurations on Mechanical

Lecture 112 Workshop 06 - Generate Mesh

Lecture 113 Workshop 06 - Define BCs and Solve Mathematical Model

Lecture 114 Workshop 06 - Post-Process Results

Lecture 115 Workshop 06 - Verification - Part 1

Lecture 116 Workshop 06 - Verification - Part 2

Section 9: Plane Strain

Lecture 117 Equations of Elasticity for Plane Strain - Part 1

Lecture 118 Equations of Elasticity for Plane Strain - Part 2

Lecture 119 Finite Element Formulation of 4-node rectangle - Part 1

Lecture 120 Finite Element Formulation of 4-node rectangle - Part 2

Lecture 121 Finite Element Formulation of 4-node rectangle - Part 3

Lecture 122 Finite Element Formulation of 4-node rectangle - Part 4

Lecture 123 Finite Element Formulation of 4-node rectangle - Part 5

Lecture 124 Numerical Integration - Gaussian Quadrature - Part 1

Lecture 125 Numerical Integration - Gaussian Quadrature - Part 2

Lecture 126 Workshop 07 - Problem Specification and Pre-analysis

Lecture 127 Workshop 07 - Creating Geometry

Lecture 128 Workshop 07 - Start setting up mathematical model

Lecture 129 Workshop 07 - Finish setting up mathematical model and solve

Lecture 130 Workshop 07 - Verification - Part 1

Lecture 131 Workshop 07 - Verification - Part 2

Lecture 132 Workshop 07 - Verification - Part 3

Lecture 133 Workshop 07 - Introduction to Singularities

Section 10: Isoparametric Formulation

Lecture 134 Isoparametric Formulation - Four node quadrilateral element - Part 1

Lecture 135 Isoparametric Formulation - Four node quadrilateral element - Part 2

Lecture 136 Isoparametric Formulation - Four node quadrilateral element - Part 3

Lecture 137 Isoparametric Formulation - Four node quadrilateral element - Part 4

Lecture 138 Isoparametric Formulation - Four node quadrilateral element - Part 5

Lecture 139 Isoparametric Formulation - Four node quadrilateral element - Exercise

Lecture 140 Isoparametric Formulation - Singularity of the Jacobian Matrix

Lecture 141 Isoparametric Formulation - Conclusion

Lecture 142 Isoparametric Formulation - Ansys Exercise

Engineering and Science Students: This course is primarily aimed at undergraduate and graduate students studying engineering disciplines, such as mechanical, civil, aerospace, or materials engineering. It's also relevant to students in related scientific fields.,Engineering Professionals: Engineers and professionals who want to deepen their understanding of the finite element method theory and gain insights into the inner workings of commercial software tools can benefit from this course.,Researchers: Researchers in engineering and scientific fields who need to use finite element analysis as part of their research projects can enhance their skills and knowledge through this course.,Career Advancers: Individuals looking to advance their careers in industries where finite element analysis is widely used, such as automotive, aerospace, structural design, and manufacturing.,Curious Learners: Anyone with a genuine interest in understanding the theoretical foundations behind engineering simulations and software tools, even if they are not pursuing formal education or a career in engineering.