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**1. General introduction to finite element method**

ME 520 Fundamentals of Finite Element Analysis 1. General introduction to finite element method Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze Technical University

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Finite Element Method: FEM Finite Element Analysis: FEA ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Course Content Finite Element Discretization Concepts Finite Element Formulations FEM Computer Applications (ANSYS Workbench) ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Computational Mechanics: Computational Mechanics branch can be separated according to problem’s physical content. Computational Mechanics Nano and Micromechanics Continium Mechanics: Solids and Stuctures, Fluids, Multiphysics Systems ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Computational Solid and Structural Mechanics Computational Solid and Structural Mechanics Statics Dynamics ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Computational Solid and Structural Mechanics: Computational Solid and Structural Mechanics Linear Nonlinear ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Solution Methods used in Computational Mechanics: Finite Element Method Finite Difference Method Boundary Element Method Finite Volume Method Mesh-Free Method ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Formulations and Solution Methods used in Finite Element Method: FEM Model Formulation FEM Model Solution Displacement Equilibrium Mixed Hybrid Stiffness Flexibility Mixed ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Summarizing: This Course Covers Computational structural mechanics Linear static problems Spatially discretized by displacement-formulated FEM Solved by the stiffness method ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Reasons of Using Finite Element Method: Design Analysis: Reduces the number of experiments and hand calculations and enables computer FEM/FEA is the commonly worldwide used analysis and simulation method Can work with CAD/CAM applications in an integrated manner ... ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Engineering Applications of Finite Element Method: Mechanics/Space/Aeronautics/Civil/Automotive Stuructural Analysis (statics/dynamics, linear/nonlinear) Heat/Fluid Electromagnetics Geomechanics Biomechanics ... ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts A Brief History of the FEM: Courant (Variational methods) Turner, Clough, Martin and Topp (Stiffness) Clough (“Finite Element”, plane problems) 1970s Applications on mainframe computers 1980s Microcomputers, pre- and postprocessors 1990s Analysis of large structural systems 2000s Mini Computer and pre- and postprocessor Apllications ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Available Commercial FEM Software Packages: ANSYS (General purpose, PC and workstations) SDRC/I-DEAS (Complete CAD/CAM/CAE package) NASTRAN DYTRAN (Nonlinear and dynamic analyses) ABAQUS (Nonlinear and dynamic analyses) COSMOS (General purpose FEA) ALGOR (PC and workstations) PATRAN (Pre/Post Processor) HyperMesh (Pre/Post Processor) Dyna-3D (Crash/impact analysis) ... ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Finite Element Method: FEM The finite element method (FEM), or finite element analysis (FEA), is based on the idea of building a complicated object with simple blocks, or, dividing a complicated object into small and manageable pieces (discretization). Elements 9 9 Finite element model consists of elements and nodes. E1: Element number 4,5,9: Node numbers Nodes E1 1 Element Finite Element Model ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts FEM in Structural Analysis Procedures: · Divide structure into pieces (elements with nodes) · Describe the behavior of the physical quantities on each element · Connect (assemble) the elements at the nodes to form an approximate system of equations for the whole structure · Solve the system of equations involving unknown quantities at the nodes (e.g., displacements) · Calculate desired quantities (e.g., strains and stresses) at selected elements ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Objectives of This FEM Course · Understand the fundamental ideas of the FEM · Know the behavior and usage of each type of elements covered in this course · Be able to prepare a suitable FE model for given problems · Can interpret and evaluate the quality of the results (know the physics of the problems) · Be aware of the limitations of the FEM (don’t misuse the FEM - a numerical tool) ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts Linear Static Analysis Many of structural engineering problems can be threated as linear static problem with the acceptance of the following assumptions. Small deformations (loading pattern do not change with deformation) Materials are elastic Loads are static (load is applied slowly and uniformly) Linear static analysis gives an idea about the behavior of the structure and can be accepted as a good approach for many of the analyses. Also for many cases static analysis is the base for nonlinear analysis. Within this course only static analysis subjects will be covered. ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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**Mechanical Engineering Department, GTU**

1. General introduction to finite element method Fundemental Concepts ME Dr. Ahmet Zafer Şenalp Mechanical Engineering Department, GTU

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