PPT-CHAP 1 STRESS-STRAIN ANALYSIS

FINITE ELEMENT ANALYSIS AND DESIGN NamHo Kim STRESS Stress Fundamental concept related to the safety of a structure Often used as criteria for mechanical design Internal force created by deforming the shape against external loads. Nonlinear Finite Element Analysis Procedures. Nam-Ho Kim. 1. Goals. What is a nonlinear problem?. How is a nonlinear problem different from a linear one?. What types of nonlinearity exist?. How to understand stresses and strains. FEA for Nonlinear Elastic Problems. Nam-Ho Kim. Table of Contents. 3.2. Stress and Strain Measures in Large Deformation. 3.3. Nonlinear Elastic Analysis. 3.4. Critical Load Analysis. 3.5. Hyperelastic Materials. FEA for . Elastoplastic. Problems. Nam-Ho Kim. Table of Contents. 4.2. 1D Elastoplasticity. 4.3. Multi-dimensional Elastoplasticity. 4.4. Finite Rotation with Objective Integration. 4.5. Finite Deformation Elastoplasticity with . Preliminary Concepts and . Linear Finite Elements. Instructor: Nam-Ho Kim (. nkim@ufl.edu. ). Web: http://www2.mae.ufl.edu/nkim/INFEM. /. Table of Contents. 1.1. . INTRODUCTION. 1.2. VECTOR AND TENSOR . FOR PLANE SOLIDS. FINITE ELEMENT ANALYSIS AND DESIGN. Nam-Ho Kim. Audio: Raphael T. Haftka. INTRODUCTION. Plane Solids. All engineering problems are 3-D. It is the engineer who approximates the problem using 1-D (beam or truss) or 2-D (plane stress or strain).. G. Vallone, P. Ferracin, C. Fichera, M. Guinchard, P. Grosclaude, D. Cheng, H. Pan, T. Strauss, G. Chlachidze. . Joint LARP / HL-LHC Annual Meeting 2016, SLAC, 19/05/2016. Acknowledgments. CERN. A. Ballarino, H. Bajas, M. Bajko, B. Bordini, J.C. Perez, S. Izquierdo Bermudez, P. . From fig 4 , the decline in the stress necessary to continue deformation past the maximum, point M, seems to indicate that the metal is becoming weaker. However, the cross-sectional area is decreasing rapidly within the neck region, where deformation is occurring. The stress, as computed from . Stress-Strain Diagram . Suppose that a metal specimen be placed in tension-compression testing machine. As the axial load is gradually increased in increments, the total elongation over the gage length is measured at each increment of the load and this is continued until failure of the specimen takes place. Knowing the original cross-sectional area and length of the specimen, the normal stress σ and the strain ε can be obtained. The graph of these quantities with the stress σ along the y-axis and the strain ε along the x-axis is called the stress-strain diagram. The stress-strain diagram differs in form for various materials. The diagram shown below is that for a medium carbon structural steel. . Asady. Al-. Mustansiryah. University . Mechanical Engineering Department. Part 1 : theory. Strain. Simple Strain. Also known as unit deformation, strain is the ratio of the change in length caused by the applied force, to the original length.. where δ is the deformation and L is the original length, thus ε is dimensionless. . Stress-Strain Diagram . Suppose that a metal specimen be placed in tension-compression testing machine. As the axial load is gradually increased in increments, the total elongation over the gage length is measured at each increment of the load and this is continued until failure of the specimen takes place. Knowing the original cross-sectional area and length of the specimen, the normal stress σ and the strain ε can be obtained. The graph of these quantities with the stress σ along the y-axis and the strain ε along the x-axis is called the stress-strain diagram. The stress-strain diagram differs in form for various materials. The diagram shown below is that for a medium carbon structural steel. . 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 . Nam-Ho Kim. Introduction. Linear systems. Infinitesimal deformation: no . significant difference between the deformed and undeformed . shapes. Stress . and strain are defined in the undeformed . shape. Problems. Nam-Ho Kim. Introduction. Elastic material: a . strain energy . is differentiated by strain to obtain stress. History-independent, potential exists, reversible, no permanent deformation. Elatoplastic. Introduction to Stress and Strain (Lesson). Mechanical Engineers characterize materials using forces, stress, and strain. They analyze the behavior of materials in order to define safety constraints. In simple terms, they need to determine how much stress can be applied before the material breaks or becomes permanently deformed. Biomedical engineers test materials to strengthen or replace tissues or broken bones..