PPT-Derivatives of static response from linear finite element a

Local search algorithms benefit from derivatives even when they are calculated by finite differences Often derivatives can be calculated at fraction of cost of finitedifference derivatives Goal of todays lecture is to show why this is usually true for static response. Page 1 of 6 www.oasys-software.com Footfall Vibration and Finite Element Analysis Introduction The possibility of human footfall loading leading to excessive vibration of structures has long been A comparison of common element types and patch test verification. By: Rachel Sorna and William . weinlandt. Objectives. . Develop a sound understanding of 3D stress analysis through derivation, construction, and implementation of our own 3D FEM Matlab Code. . Mechanics Problems. Rafi Muhanna. School of Civil and Environmental Engineering. Georgia Institute of Technology, . Atlanta, GA 30332-0355, . USA. Robert L. Mullen. Department of Civil and Environmental Engineering. 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. and Differential Equations. Differentiation. Differential change . 4/21/2010. 2. Derivative Definition. 4/21/2010. 3. Taylor Series. 4/21/2010. 4. Taylor Series Graphically. . 4/21/2010. 5. Numerical Differentiation Based on Taylor Series . 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. Dr. Ahmet Zafer . Şenalp. e-mail: . azsenalp@gmail.com. Mechanical Engineering Department. Gebze. Technical University. ME 520. Fundamentals of . Finite. Element Analysis. The linear tetrahedral (solid) element is a three-dimensional finite element with . 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. Rayleigh-Ritz method approximate solution in the entire beam. Difficult to find good approximate solution (discontinuities in derivatives). Finite element approximates solution in an element. In a small element simple functions are acceptably accurate. 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 . Abaqus. Instructor. : Nam-Ho Kim (nkim@ufl.edu). Abaqus. Basics. Simulation. Abaqus. /Standard. Output file:. Job.odb, job.dat. Postprocessing. Abaqus. /CAE. Preprocessing. Abaqus. /CAE. Interactive Mode. 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 .