Martinec-ContinuumMechanics.pdf

... the material body. A material body B = {X } is a compact measurable set of an infinite number of material elements X , called the material particles or material points, that can be placed in a one-to-one correspondence with triplets of real numbers. Such triplets are sometimes called the intrinsic c ...

... the material body. A material body B = {X } is a compact measurable set of an infinite number of material elements X , called the material particles or material points, that can be placed in a one-to-one correspondence with triplets of real numbers. Such triplets are sometimes called the intrinsic c ...

Two Interpretations of Rigidity in Rigid Body Collisions

... time, the relative displacement between pairs of points that are not in the contact-deformation regions (say points R and P) can be accurately calculated by treating the spheres as rigid everywhere except in a small, localized contact region governed by the Hertz relations. In general point-contact ...

... time, the relative displacement between pairs of points that are not in the contact-deformation regions (say points R and P) can be accurately calculated by treating the spheres as rigid everywhere except in a small, localized contact region governed by the Hertz relations. In general point-contact ...

Two Interpretations of Rigidity in Rigid Body Collisions

... { for which the distances betweenC points ,R , andP stay xed { does not lead to a unique outcome Consider the system in Fig. 4a colliding with a rigid wall as in Fig. 4b. In this case, of compression at the end of which the block is momentarily at rest, followed by a period or rebound during which t ...

... { for which the distances betweenC points ,R , andP stay xed { does not lead to a unique outcome Consider the system in Fig. 4a colliding with a rigid wall as in Fig. 4b. In this case, of compression at the end of which the block is momentarily at rest, followed by a period or rebound during which t ...

BALANCE PRINCIPLES

... This chapter presents the basic dynamical equations for continuum mechanics and some key inequalities from thermodynamics. The latter may be used to give functional form to the second Piola-Kirchhoff stress tensor-a fundamental ingredient in the dynamical equations. The study of this functional form ...

... This chapter presents the basic dynamical equations for continuum mechanics and some key inequalities from thermodynamics. The latter may be used to give functional form to the second Piola-Kirchhoff stress tensor-a fundamental ingredient in the dynamical equations. The study of this functional form ...

Stress

... life, is always a result of shear stress acting in the contact areas between material bodies. The integrity of a solid body is largely secured by internal shear stresses. The two major classes of materials, fluids and solids, react differently to external stresses. Whereas fluids respond by flowing, ...

... life, is always a result of shear stress acting in the contact areas between material bodies. The integrity of a solid body is largely secured by internal shear stresses. The two major classes of materials, fluids and solids, react differently to external stresses. Whereas fluids respond by flowing, ...

Module 8

... – the material on this side of this surface is exerting a force on the material on the other side of the surface. Now, this concept of surface forces seems like a simple one to us, but it comes from something called the Cauchy Stress Principle, which we will examine a statement of right now. The Ca ...

... – the material on this side of this surface is exerting a force on the material on the other side of the surface. Now, this concept of surface forces seems like a simple one to us, but it comes from something called the Cauchy Stress Principle, which we will examine a statement of right now. The Ca ...

Dynamic Simulation of Non-penetrating Flexible Bodies

... In this paper we present a new formulation for the dynamics of flexible bodies that covers collisions and continuous contact as well as free motion. The model, which draws on the flexible-body model proposed by Witkin and Welch[9] and on the analytical contact force model for rigid bodies presented ...

... In this paper we present a new formulation for the dynamics of flexible bodies that covers collisions and continuous contact as well as free motion. The model, which draws on the flexible-body model proposed by Witkin and Welch[9] and on the analytical contact force model for rigid bodies presented ...

Mechanical Engineering: Module 8

... and the statement is the following. Upon any imagined closed surface S, closed surface, there exists a distribution of stress vectors (we are going to call those stress vectors t. We will be using t for something else later, but for right now it is the stress vector), whose resultant and moment are ...

... and the statement is the following. Upon any imagined closed surface S, closed surface, there exists a distribution of stress vectors (we are going to call those stress vectors t. We will be using t for something else later, but for right now it is the stress vector), whose resultant and moment are ...

Stress

... waves propagate with different velocities in different rocks. When an initial seismic waves coming from the source point arrive at a contact of two different rocks, they split into several waves propagating in different directions with different velocities. Some of them will get back to the surface ...

... waves propagate with different velocities in different rocks. When an initial seismic waves coming from the source point arrive at a contact of two different rocks, they split into several waves propagating in different directions with different velocities. Some of them will get back to the surface ...

B-1 - Fontys

... returns 1 if body #3’s y position equals 3.0. This formula does not set any values of body #3’s position. Takes two numbers and returns the value 1 if the two values are not equal. Otherwise, returns the value 0. ...

... returns 1 if body #3’s y position equals 3.0. This formula does not set any values of body #3’s position. Takes two numbers and returns the value 1 if the two values are not equal. Otherwise, returns the value 0. ...

Engineering Mechanics

... Models are generally used in science and engineering to reduce a complex reality for detailed investigations. The prediction of a future state of a system is the main goal, which has to be achieved. Due to the hypothetical nature of this approach, it is irrelevant whether the assumed state will be a ...

... Models are generally used in science and engineering to reduce a complex reality for detailed investigations. The prediction of a future state of a system is the main goal, which has to be achieved. Due to the hypothetical nature of this approach, it is irrelevant whether the assumed state will be a ...

B-1 - Interactive Physics

... in the x position field. When you run the simulation, the body will start at x = 2.3 and then move to the right. If you type a formula in any of the three velocity fields, the values in the position fields will only be used as initial conditions. For example, if Vx = time and x = 3.0 , the center of ...

... in the x position field. When you run the simulation, the body will start at x = 2.3 and then move to the right. If you type a formula in any of the three velocity fields, the values in the position fields will only be used as initial conditions. For example, if Vx = time and x = 3.0 , the center of ...

Stress, Strain, Virtual Power and Conservation Principles

... In vector and tensor calculus, subscript and superscript index notation is used to denote collections of variables, for instance, the set x1 ; x2 ; :::; xn is denoted by xi ; i = 1; 2; :::; n or by xi ; i = 1; 2; :::; n. Likewise, the set y 1 ; y 2 ; :::; y n is denoted as y j ; j = 1; 2; :::; n. N ...

... In vector and tensor calculus, subscript and superscript index notation is used to denote collections of variables, for instance, the set x1 ; x2 ; :::; xn is denoted by xi ; i = 1; 2; :::; n or by xi ; i = 1; 2; :::; n. Likewise, the set y 1 ; y 2 ; :::; y n is denoted as y j ; j = 1; 2; :::; n. N ...

Stress, Strain, Virtual Power and Conservation Principles

... Ars∗ = gr∗ · gm gs∗ · gn Amn and Amn = gr∗ · gm gs∗ · gn Amn∗ ...

... Ars∗ = gr∗ · gm gs∗ · gn Amn and Amn = gr∗ · gm gs∗ · gn Amn∗ ...

Materialy/01/Applied Mechanics-Lectures/Applied Mechanics

... Physical properties - continuous functions of spatial variables. The earth - inertial reference frame - allowing application of Newton´s laws. Gravity is only external force field. Relativistic effects are ignored. The systems considered are not subject to nuclear reactions, chemical reactions, exte ...

... Physical properties - continuous functions of spatial variables. The earth - inertial reference frame - allowing application of Newton´s laws. Gravity is only external force field. Relativistic effects are ignored. The systems considered are not subject to nuclear reactions, chemical reactions, exte ...

CTE3-Script.pdf

... Continuum Mechanics is the branch of mechanics used to investigate the deformation and flow of materials subjected to loads. Is a generalization of the classical Newtonian mechanics to macroscopic bodies. These bodies are considered formed by infinite collections of material points. As in classical ...

... Continuum Mechanics is the branch of mechanics used to investigate the deformation and flow of materials subjected to loads. Is a generalization of the classical Newtonian mechanics to macroscopic bodies. These bodies are considered formed by infinite collections of material points. As in classical ...

Suggested solutions to 2015 MEK2500 Mock Exam

... Suggested solutions to 2015 MEK2500 Mock Exam November 25, 2015 Oppgave 1 a) The displacement (in Lagrange representation) is: u(x) = f (x) − x ...

... Suggested solutions to 2015 MEK2500 Mock Exam November 25, 2015 Oppgave 1 a) The displacement (in Lagrange representation) is: u(x) = f (x) − x ...