Introduction to Elasticity
Introduction to Elasticity
Outline. What is Elasticity?: A Brief History of Elasticity? Tools of the Trade? Engineering Applications of Elasticity? Fundamental Concepts in Elasticity: Assumptions of Elasticity Theory? Geometry of Elastic Solids. Topics That Will Be Covered· Greek Alphabet2
Outline • What is Elasticity? • A Brief History of Elasticity • Tools of the Trade • Engineering Applications of Elasticity • Fundamental Concepts in Elasticity • Assumptions of Elasticity Theory • Geometry of Elastic Solids • Topics That Will Be Covered • Greek Alphabet 2
What is Elasticity?? Concerned with determining stress, strain, anddisplacement distribution in an elastic solid under theinfluence of external forces.FALLinearly ElasticElastic. Using continuum mechanics formulation establishesa mathematical boundary value problem model - aset of governing partial differential field equationswith particular boundary conditions3
• Concerned with determining stress, strain, and displacement distribution in an elastic solid under the influence of external forces. 3 What is Elasticity? Linearly Elastic F ΔL Elastic F ΔL • Using continuum mechanics formulation establishes a mathematical boundary value problem model - a set of governing partial differential field equations with particular boundary conditions
History of Elasticity? Started from early 19th century, primarily by Navier,Cauchy, Saint-Venant, Love, Muskhelisvili.Kirchhoff, Poisson,. Needed for understanding the deformation anddamage mechanisms of bridges, roads, shipsmilitary weapons, and etc: Understanding optical wave propagation requireselastic wave theory.4
• Started from early 19th century, primarily by Navier, Cauchy, Saint-Venant, Love, Muskhelisvili, Kirchhoff, Poisson, . • Needed for understanding the deformation and damage mechanisms of bridges, roads, ships, military weapons, and etc. • Understanding optical wave propagation requires elastic wave theory. 4 History of Elasticity
History of Elasticity: Claude-L0uis Navier (1785-1836): Unified the theory for beam bending (1826).. Founder of Continuum Mechanics: submittedtwo monographs to French Academy ofScience in 1821.: Derived the equations of equilibrium andmotion for elastic and isotropic solidsC(V2u, + 2uj,jt)+ F, = 0: Promoted the method allowable stress forexamining the strength condition.: There is only one elastic constant in hisformulations and no stress and strain concepts5
5 • Claude-Louis Navier (1785−1836) • Unified the theory for beam bending (1826). • Founder of Continuum Mechanics: submitted two monographs to French Academy of Science in 1821. • Derived the equations of equilibrium and motion for elastic and isotropic solids. • Promoted the method allowable stress for examining the strength condition. • There is only one elastic constant in his formulations and no stress and strain concepts. 2 , 2 0 C u u F i j ji i History of Elasticity