The Finite Element Method For Linear Structural Analysis

What you'll learn
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.
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 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 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 LugModule 12: Shell Elements- Plate Element Theory- Plate Element Formulation- Shell Element Theory- Workshop 10: Thin Folded PlateThroughout 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 Course Material
Lecture 2 Introduction - Part 1
Lecture 3 Introduction - Part 2
Lecture 4 Introduction - Part 3
Lecture 5 Abaqus Instalation Guide
Lecture 6 Workshop 01 - Connecting Lug - Problem Specification
Lecture 7 Workshop 01 - Connecting Lug - Pre-analysis
Lecture 8 Workshop 01 - Connecting Lug - Create Domain
Lecture 9 Workshop 01 - Connecting Lug - Mesh the Domain
Lecture 10 Workshop 01 - Connecting Lug - Create Material and Instance
Lecture 11 Workshop 01 - Connecting Lug - Apply BCs and Solve BVP
Lecture 12 Workshop 01 - Connecting Lug - Verification - Part 1
Lecture 13 Workshop 01 - Connecting Lug - Verification - Part 2
Lecture 14 Workshop 01 - Connecting Lug - Verification - Part 3
Lecture 15 Workshop 01 - Connecting Lug - Convergence Study
Section 2: Linear Elastic Spring Element
Lecture 16 Linear Elastic Spring Element - Part 1
Lecture 17 Linear Elastic Spring Element - Part 2
Lecture 18 Linear Elastic Spring Element - Part 3
Lecture 19 System Assembly in Global Coordinates - Part 1
Lecture 20 System Assembly in Global Coordinates - Part 2
Lecture 21 Exercises - Part 1
Lecture 22 Exercises - Part 2
Lecture 23 Workshop 02 - Spring Element - Pre-analysis
Lecture 24 Workshop 02 - Spring Element - Define Domain
Lecture 25 Workshop 02 - Spring Element - Define BCs and Governing Equations
Lecture 26 Workshop 02 - Spring Element - Verification
Lecture 27 Workshop 02 - Spring Element - Study Input File
Section 3: Linear Elastic Bar Element
Lecture 28 Elastic Bar Element - Part 1
Lecture 29 Elastic Bar Element - Part 2
Lecture 30 Elastic Bar Element - Part 3
Lecture 31 Exercise - Part 1
Lecture 32 Exercise - Part 2
Lecture 33 Exercise - Part 3
Lecture 34 Strain Energy
Lecture 35 Castigliano's First Theorem - Part 1
Lecture 36 Castigliano's First Theorem - Part 2
Lecture 37 Minimum Potential Energy - Part 1
Lecture 38 Minimum Potential Energy - Part 2
Lecture 39 Workshop 03 - Bar Element - Problem Specification
Lecture 40 Workshop 03 - Bar Element - Pre-Analysis
Lecture 41 Workshop 03 - Bar Element - Define Domain
Lecture 42 Workshop 03 - Bar Element - Setup BCs and Define Governing Equation
Lecture 43 Workshop 03 - Bar Element - Post-Processing
Lecture 44 Workshop 03 - Bar Element - Analyse input file
Section 4: Truss Structures
Lecture 45 Nodal Equilibrium Equations - Part 1
Lecture 46 Nodal Equilibrium Equations - Part 2
Lecture 47 Element Transformation
Lecture 48 Direct Assembly of Global Stiffness Matrix - Part 1
Lecture 49 Direct Assembly of Global Stiffness Matrix - Part 2
Lecture 50 Direct Assembly of Global Stiffness Matrix - Part 3
Lecture 51 Boundary Conditions, Constraint Forces
Lecture 52 Element Strain and Stress - Part 1
Lecture 53 Element Strain and Stress - Part 2
Lecture 54 Comprehensive Example - Part 1
Lecture 55 Comprehensive Example - Part 2
Lecture 56 Comprehensive Example - Part 3
Lecture 57 Three dimensional Trusses - Part 1
Lecture 58 Three dimensional Trusses - Part 2
Lecture 59 Workshop 04 - Problem Specification
Lecture 60 Workshop 04 - Pre-analysis
Lecture 61 Workshop 04 - Define BPV - Part 1
Lecture 62 Workshop 04 - Define BPV - Part 2
Lecture 63 Workshop 04 - Verification
Lecture 64 Workshop 04 - Input File
Section 5: Beam Element
Lecture 65 Elementary Beam Theory - Part 1
Lecture 66 Elementary Beam Theory - Part 2
Lecture 67 Elementary Beam Theory - Part 3
Lecture 68 Beam Element
Lecture 69 Beam Element Stiffness Matrix - Part 1
Lecture 70 Beam Element Stiffness Matrix - Part 2
Lecture 71 Element Load Vector and Exercise
Lecture 72 Work Equivalence for Distributed Loads - Part 1
Lecture 73 Work Equivalence for Distributed Loads - Part 2
Lecture 74 Flexure Element with Axial Loading - Part 1
Lecture 75 Flexure Element with Axial Loading - Part 2
Lecture 76 Flexure Element with Axial Loading - Part 3
Lecture 77 A General Three-Dimensional Beam Element - Part 1
Lecture 78 A General Three-Dimensional Beam Element - Part 2
Lecture 79 Workshop 05 - Problem Specification
Lecture 80 Workshop 05 - Pre-analysis
Lecture 81 Workshop 05 - BPV Definition - Part 1
Lecture 82 Workshop 05 - BPV Definition - Part 2
Lecture 83 Workshop 05 - BPV Definition - Part 3
Lecture 84 Workshop 05 - Verification
Lecture 85 Workshop 05 - Analyse Stress and Displacement
Section 6: Equations of Elasticity
Lecture 86 Strain-Displacement Relations
Lecture 87 Stress-Strain Relations
Lecture 88 Equilibrium Equations
Lecture 89 Summary
Section 7: Matrix Mathematics and Solution Techniques for Linear Algebraic Equations
Lecture 90 Matrix Mathematics - Basic Definitions
Lecture 91 Matrix Mathematics - Simple Matrix Operations
Lecture 92 Matrix Mathematics - The Determinant of a Matrix
Lecture 93 Matrix Mathematics - The Inverse of Matrix
Lecture 94 Solution Techniques for Linear Algebraic Equations - Gauss Elimination
Lecture 95 Solution Techniques for Linear Algebraic Equations - LU Decomposition
Lecture 96 Solution Techniques for Linear Algebraic Equations - Gauss Seidel Method
Section 8: Plane Stress
Lecture 97 Equations of Elasticity for Plane Stress
Lecture 98 Finite Element Formulation Constant Strain Triangle - Part 1
Lecture 99 Finite Element Formulation Constant Strain Triangle - Part 2
Lecture 100 Finite Element Formulation Constant Strain Triangle - Part 3
Lecture 101 Summary and Stiffness Matrix Evaluation
Lecture 102 Distributed Loads - Part 1
Lecture 103 Distributed Loads - Part 2
Lecture 104 Body Forces - Part 1
Lecture 105 Body Forces - Part 2
Lecture 106 Workshop 06 - Pre-analysis
Lecture 107 Workshop 06 - BVP Definition - Part 1
Lecture 108 Workshop 06 - BVP Definition - Part 2
Lecture 109 Workshop 06 - Symmetry Condition
Lecture 110 Workshop 06 - Convergence Study
Lecture 111 Workshop 06 - End of Verification
Lecture 112 Workshop 06 - Final Comments
Section 9: Plane Strain
Lecture 113 Equations of Elasticity for Plane Strain
Lecture 114 Finite Element Formulation Four-node Rectangle - Part 1
Lecture 115 Finite Element Formulation Four-node Rectangle - Part 2
Lecture 116 Finite Element Formulation Four-node Rectangle - Part 3
Lecture 117 Finite Element Formulation Four-node Rectangle - Part 4
Lecture 118 Numerical Integration Gaussian Quadrature - Part 1
Lecture 119 Numerical Integration Gaussian Quadrature - Part 2
Lecture 120 Workshop 07 - Pre-Analysis
Lecture 121 Workshop 07 - Define BVP
Lecture 122 Workshop 07 - Shear Locking
Lecture 123 Workshop 07 - Hourglass and Incompatible mode elements
Lecture 124 Workshop 07 - Numerical Singularity
Section 10: Isoparametric Formulation
Lecture 125 Four-node quadrilateral element - Part 1
Lecture 126 Four-node quadrilateral element - Part 2
Lecture 127 Four-node quadrilateral element - Part 3
Lecture 128 Exercise
Lecture 129 Singularity of the Jacobian Matrix
Lecture 130 Workshop 08 - Pre-analysis
Lecture 131 Workshop 08 - Define BVP
Lecture 132 Workshop 08 - Post-Processing
Section 11: General Three Dimensional Stress Element
Lecture 133 Introduction and Equations of Elasticity
Lecture 134 Finite Element Formulation
Lecture 135 Example: 4-node Tetrahedral
Lecture 136 Stress and Strain Computation - Stress vs Strain Curve
Lecture 137 Stress and Strain Computation - Maximum shear stress theory
Lecture 138 Stress and Strain Computation - Distortion Energy Theory
Lecture 139 Workshop 09 - Pre-analysis
Lecture 140 Workshop 09 - Define BVP - Part 1
Lecture 141 Workshop 09 - Define BVP - Part 2
Lecture 142 Workshop 09 - Post-Processing
Section 12: Shell Element
Lecture 143 Plate Element Theory
Lecture 144 Plate Element Formulation
Lecture 145 Shell Element Formulation
Lecture 146 Workshop 10 - Skew Plate
Lecture 147 Extra 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.
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