2D Strain/Stress Analysis in FEA | FEA Done Right – Section 5

How does finite element analysis convert nodal displacements into the strains and stresses engineers use to evaluate a design? In Section 5 of the FEA Done Right Series, we follow this process step by step: Displacement → Strain → Stress We begin with strain–displacement relationships in 1D, 2D, and 3D. We then introduce the L matrix and derive the strain–displacement matrix, B, using shape functions: ε = LU = LNa = Ba Next, we use the material constitutive matrix, D, to calculate stress: σ = Dε You will also learn why a linear triangular element produces constant strain and stress, why it is called a Constant Strain Triangle (CST), and what limitations this creates. Finally, we complete a numerical example and calculate the strain and stress inside a CST element under plane-stress conditions. 📘 DETAILED MECHCADEMY NOTE: 2D ANALYSIS IN ELASTICITY For a deeper explanation of plane stress, plane strain, and axisymmetric analysis—including the governing assumptions, strain and stress components, and constitutive matrices—visit the MechCADemy page: https://www.salehinia-cmsml.com/mechc... ▶️ FEA Done Right Series playlist:    • FEA Done Right Series   New sections of the FEA Done Right Series are released regularly. Subscribe and turn on notifications so you do not miss the next section. ABOUT THE INSTRUCTOR Dr. Iman Salehinia Associate Professor of Mechanical Engineering Northern Illinois University, DeKalb, USA CHAPTERS 00:00 Introduction 02:28 Strain–Displacement Relations in 1D, 2D, and 3D 04:28 The L Matrix in 2D 05:23 From Shape Functions to the B Matrix 06:54 B Matrix for a Linear Triangular Element 07:57 Why CST Elements Have Constant Strain 09:35 From Strain to Stress in 1D and 3D 10:50 Stress–Strain Relations in 2D: Plane Stress 13:01 Worked Constant Strain Triangle Example 14:31 Stiffness Matrices and What Comes Next If you found this video useful, please like it, subscribe to MechCADemy, and share it with students and engineers who want to understand FEA beyond simply operating the software. #FiniteElementAnalysis #FEA #FiniteElementMethod #MechanicalEngineering #CivilEngineering #StructuralEngineering #AerospaceEngineering #ComputationalMechanics #EngineeringEducation #MechCADemy