PPT-ME 160 Introduction to Finite Element Method-Spring 2016

Topics for Term Projects by Teams of 2 Students Instructor TaiRan Hsu Professor Dept of Mechanical engineering San Jose State University San Jose CA USA TwoTier p rojects for students in ME 160 class. 1 Introduction Objectives In this section you will learn the following Introduction brPage 2br Module 3 Method of Analyses Lecture 15 Finite Element Method Section 151 Introduction INTRODUCTION The finite element method is the representation of Local search algorithms benefit from derivatives even when they are calculated by finite differences. Often derivatives can be calculated at fraction of cost of finite-difference derivatives. Goal of today’s lecture is to show why this is usually true for static response. Chapter 2. Finite Element Analysis (F.E.A.) of 1-D Problems. Historical Background . Hrenikoff, 1941 – “frame work method” . Courant, 1943 – “piecewise polynomial interpolation” . Turner, 1956 – derived stiffness matrices for truss, beam, etc. BEAMS. Austin Cosby . and . Ernesto Gutierrez-. Miravete. Rensselaer at Hartford. Euler-Bernoulli Beam . Theory. The beam has uniform properties. The beam is slender (L/h is small). The beam obeys Hooke’s Law. By . S . Ziaei-Rad. Mechanical Engineering Department, IUT. FEM Basic FEATURES. T. he finite . element method has the following three . basic . features. :. 1. Divide the whole (i.e. domain) into parts, called . Agenda. PART I. Introduction and Basic Concepts. 1.0 Computational Methods. 1.1 Idealization. 1.2 Discretization. 1.3 Solution. 2.0 The Finite Elements Method. 2.1 FEM Notation. 2.2 Element Types. AND MODELING. FINITE ELEMENT ANALYSIS AND DESIGN. Nam-Ho Kim. INTRODUCTION. When a physical problem statement is given, how can we model and solve it using FEA?. David Cowan (2007). FINITE ELEMENT PROCEDURE. Stephen Kirkup. School of Engineering, . University of Central Lancashire, England. Purpose. The Boundary Element Method is a Numerical Method. From a mathematical viewpoint the BEM finds an approximate solution to a partial differential equation (PDE) governing a domain. By . S . Ziaei-Rad. Mechanical Engineering Department, IUT. FEM Basic FEATURES. T. he finite . element method has the following three . basic . features. :. 1. Divide the whole (i.e. domain) into parts, called . Jacob Fish and Zheng Yuan Departments of Civil, Mechanical and Aerospace Engineerinh Rensselaer Polytechnic Institute Troy, NY 12180, USA fishj@rpi.edu Abstract 1. Introduction This manuscript J.N. Reddy\'s, An Introduction to the Finite Element Method, third edition is an update of one of the most popular FEM textbooks available. The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering application areas.Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world.A supplementary text Web site located at http: //www.mhhe.com/reddy3e contains password-protected solutions to end-of-chapter problems, general textbook information, supplementary chapters on the FEM1D and FEM2D computer programs, and more! Key Features Approximately 30% of the problems have been revised or are new to this edition. Approximately 30% of the problems have been revised or are new to this edition. Approximately 30% of the problems have been revised or are new to this edition. Do you want to solve problems that have not been solved many times before? New tools create modern learning. Do you want your text to include a large number of diverse example problems? Worked examples help students understand and apply theory to actual problems, and with application-based examples they see the ties between FEM methods and real engineeing analysis. Strong coverage of FEM\'s mathematical foundations. Do you want your text to have a good balance between theory and application? The book will retain Reddy\'s precise explanation of FEM\'s mathematical workings, always seen as a strong point of the book. In the 3/e it will be in good balance with practical applications. Comprehensive coverage of material from general field problems as well heat transfer, fluid mechanics, and solid and structural mechanics (bars, beams, frames, plane elasticity and plate bending). This makes the text approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world. Do you want a text that can relate to all disciplines, not just structural engineering? The author\'s writing style is clear and his explanation plenty. Due to the authors consistent, easy-to-understand writing style, students can gain understanding of the material the first time it is reviewed. The previous Chapter 3, Second-Order Boundary Value Problems, has been split into two chapters for the third edition. Chapter 3 i FINITE . ELEMENT ANALYSIS AND DESIGN. Nam-Ho . Kim. INTRODUCTION. We learned . Direct Stiffness Method. in Chapter 2. Limited to simple elements such as 1D bars. In Chapter 3, . Galerkin. Method. and . FINITE . ELEMENT ANALYSIS AND DESIGN. Nam-Ho . Kim. INTRODUCTION. Direct stiffness method is limited for simple 1D problems. FEM can be applied to many engineering problems that are governed by a differential equation.