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Finite Element Analysis : Solving Bar, Truss & Beam Problems
73 students

Finite Element Analysis : Solving Bar, Truss & Beam Problems

Finite Element Analysis Made Easy: Solving Bar, Truss & Beam Problems Step-by-Step
Created byRajan Gosavi (Gold Medalist , M.Tech. )
Last updated 12/2025
English

What you'll learn

  • Formulate and solve 1D, 2D, and beam element FEA problems manually
  • Develop and assemble stiffness matrices and load vectors
  • Analyze and interpret displacement, reaction, and stress results
  • Apply the Finite Element Method confidently in practical engineering problems

Course content

3 sections • 16 lectures • 2h 57m total length

  • Introduction to the course2:26

    Explore finite element analysis basics, forming the element and global stiffness matrices, computing nodal deflections and reactions, and solving bar, beam, and truss examples with discretization and boundary conditions.

  • How to formulate the Global Stiffness Matrix9:13

    Learn how to formulate the global stiffness matrix by assembling element stiffness matrices, applying boundary conditions, and deriving reactions and displacements in bar and beam problems.

  • Example 18:04

    demonstrates using the finite element method to compute nodal displacements in a three-spring system, builds the global stiffness matrix, and solves for u2, u3 and the fixed-node reaction.

  • Example 211:48

    Solve a finite element analysis of a metallic bar under axial loading, derive element stiffness and the global stiffness matrix, compute nodal displacements and support reaction, and determine element stresses.

  • Example 311:01

    Explore a finite element analysis of a stepped aluminium-steel bar under axial 200 kN, computing nodal displacement, element stresses, and support reactions using a 3-node global stiffness approach.

  • Example 48:31

    Model a tapered steel plate with two linear finite elements, discretize areas to 700 and 500 mm², assemble the stiffness, solve for u2 and u3, and find the support reaction.

  • Example 56:54

    Apply the finite element method to a three-node spring system with five springs. Assemble the global stiffness matrix, apply boundary conditions, and solve for nodal displacements and reactions.

  • Example 613:18

    This example analyzes a one-dimensional tapered steel bar modeled with three finite elements, fixed at one end and loaded by 35 kN, to compute nodal displacements, reactions, and stresses.

  • Example 76:29

    Apply the finite element method to compute nodal displacements in a three-node, four-element spring network and build the global stiffness matrix from k1–k4.

  • Example 810:17

    Apply finite element analysis to a two-element bar under axial load, determine nodal displacements, stresses, and support reactions, using stiffness matrices, boundary conditions, and Hooke's law.

  • Example 914:12

    Model a thin plate with two spar elements to build the global stiffness matrix, compute nodal displacements and reactions, and evaluate element stresses using Hooke's law.

Requirements

  • Conceptual understanding of strength of materials and mechanics

Description

Finite Element Analysis (FEA) is one of the most powerful numerical techniques used in structural, mechanical, and aerospace engineering to analyze stresses, deflections, and load distribution in real-world structures. Yet, for many learners, the mathematical formulation behind FEA often feels abstract and difficult to apply.

This course — “Finite Element Analysis Made Easy” — bridges that gap. It is designed specifically to help students and professionals understand how to solve FEA problems manually and conceptually for basic structural elements such as bars, trusses, and beams, in a clear, logical, and easy-to-follow manner.

Through carefully selected solved examples and detailed explanations, you’ll learn step-by-step how to derive stiffness matrices, apply boundary conditions, assemble the global stiffness matrix, and interpret results — exactly the way it’s done in professional analysis and design workflows.

Each module focuses on developing both theoretical understanding and problem-solving ability, preparing you for academic exams, GATE preparation, or practical engineering applications.

  1. Fundamentals of Finite Element Method (FEM) and its significance in structural analysis

  2. Derivation and application of stiffness matrices for:

    • Bar (1D element) under axial loading

    • Plane truss (2D element) with multiple members

    • Beam element under bending loads

  3. Step-by-step manual solution of FEA problems with systematic procedures

  4. Assembly of global stiffness matrix and enforcement of boundary conditions

  5. Computation of nodal displacements, reaction forces, and element stresses

  6. Logical explanation of matrix formulation and load vector development

  7. Conceptual clarity for GATE, university exams, and professional design practice

Who this course is for:

  • Suitable for both academic learners and industry professionals aiming to refresh their fundamentals.

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