PPT-Finite element method for structural dynamic and stability analyses

1 Prof C S Manohar Department of Civil Engineering IISc Bangalore 560 012 India Assignments 2 Problem 1 Formulate the equation of motion for the systems shown below Do not assume small displacements. 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 The unsymmetric finite element formulation and variational incorrectnesswhere ) is the bilinear symmetric functional and () is the integral over the systemdomain . Note that this statement is made ov 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. Lectures notes modified. from Alicia Kim, University of Bath, UK and Mike . Xie. RMIT Australia. 2. KKT Conditions for Topology Optimisation. 3. KKT Conditions (cont’d). Strain energy density should be . 1. Prof C S . Manohar. Department of Civil Engineering. IISc. , Bangalore 560 012 India. . Assignments. 2. Problem 1. Formulate the equation of motion for the systems shown below. Do not assume small displacements. 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. Topics for Term Projects by Teams of 2 Students. Instructor: Tai-Ran Hsu, Professor, Dept. of Mechanical engineering, San Jose State University, San Jose, CA, USA. Two-Tier . p. rojects for students in ME 160 class. 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 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.