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

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Finite Element Method: FEM Finite Element Analysis: FEA Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 2Mechanical Engineering Department, GTU 1. General introduction to finite element method

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Course Content Finite Element Discretization Concepts Finite Element Formulations FEM Computer Applications (ANSYS Workbench) Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 3Mechanical Engineering Department, GTU 1. General introduction to finite element method

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Computational Mechanics: Computational Mechanics branch can be separated according to problem’s physical content. Computational Mechanics Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 4Mechanical Engineering Department, GTU 1. General introduction to finite element method Nano and Micromechanics Continium Mechanics: Solids and Stuctures, Fluids, Multiphysics Systems

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Computational Solid and Structural Mechanics Computational Solid and Structural Mechanics Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 5Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method Statics Dynamics

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Computational Solid and Structural Mechanics: Computational Solid and Structural Mechanics Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 6Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method Linear Nonlinear

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Solution Methods used in Computational Mechanics: Finite Element Method Finite Difference Method Boundary Element Method Finite Volume Method Mesh-Free Method Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 7Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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Formulations and Solution Methods used in Finite Element Method: FEM Model Formulation FEM Model Solution Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 8Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method Displacement Equilibrium Mixed Hybrid Stiffness Flexibility Mixed

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Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 9Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method Summarizing: This Course Covers Computational structural mechanics Linear static problems Spatially discretized by displacement-formulated FEM Solved by the stiffness method

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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 ... Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 10Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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Engineering Applications of Finite Element Method: Mechanics/Space/Aeronautics/Civil/Automotive Stuructural Analysis (statics/dynamics, linear/nonlinear) Heat/Fluid Electromagnetics Geomechanics Biomechanics ... Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 11Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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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 Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 12Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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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) ... Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 13Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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9 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). Finite Element Method: FEM ME 520 Dr. Ahmet Zafer Şenalp 14Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method Finite Element Model Elements Nodes 1 Element Finite element model consists of elements and nodes. E1: Element number 4,5,9: Node numbers 9 E1

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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 Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 15Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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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) Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 16Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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Linear Static Analysis Many of structural engineering problems can be threated as linear static problem with the acceptance of the following assumptions. 1.Small deformations (loading pattern do not change with deformation) 2.Materials are elastic 3.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. Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 17Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 18Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 19Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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Fundemental Concepts ME 520 Dr. Ahmet Zafer Şenalp 20Mechanical Engineering Department, GTU 1. General introduction to finite element method 1. General introduction to finite element method

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