Full Answer
What is a rigid body?
A Rigid Body is generally defined as a body on which the distance between two points never changes whatever be the force applied on it. Or in other words, it can be said that the body which does not deform under the influence of forces is known as a Rigid Body.
What is general motion of a rigid body?
A general motion of a rigid body is one in which the body may not have a fixed point. In this case, it is easy to argue that a uniform translation of the reference configuration can be imposed on the rigid body such that any one of its material points, say, , is placed at its location in the current configuration .
How does the assumption that the bodies are rigid simplify the analysis?
The assumption that the bodies are rigid, which means that they do not deform under the action of applied forces, simplifies the analysis by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body.
What are boundary conditions for rigid bodies?
Boundary conditions for rigid bodies should be defined as described in Boundary conditions in Abaqus/Standard and Abaqus/Explicit at the rigid body reference node. Reaction forces and moments can be recovered for all degrees of freedom that are constrained at the reference node.
What is meant by a rigid body?
A rigid body is a body that does not deform or vibrate. Continuum mechanics deals with deformable bodies, as opposed to rigid bodies. A rigid body is one where every atom is always in the same position with respect to every other atom in the body , even when outside forces are applied to the body.
What is rigid body used for?
Rigidbodies are components that allow a GameObject to react to real-time physics. This includes reactions to forces and gravity, mass, drag and momentum. You can attach a Rigidbody to your GameObject by simply clicking on Add Component and typing in Rigidbody2D in the search field.
What are some examples of rigid bodies?
– Examples: Smoke, Fire, Water, Wind, Leaves, Cloth, Magnets, Flocks, Fish, Insects, Crowds, etc.
What is meant by rigid body dynamics?
Rigid body dynamics is the study of the motion in space of one or several bodies in which deformation is neglected.
What is the difference between rigid and non-rigid body?
(a) When a force is applied on a rigid body, it does not change the interspacing of constituent molecules and the dimension, which can cause motion in it. (b) When a force is applied on a non-rigid body, it changes the interspacing between its constituent molecules and dimension, which can produce motion in it.
What are the characteristics of rigid body?
In physics, a rigid body (also known as a rigid object) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it.
What are examples of rigid materials?
Rigid MaterialsAluminum.Coroplast.Duraplast.EPANEL – Aluminium Panel.Foamcore.PlexiGlass.Lexan Polycarbonate.PVC Sintra.More items...
Is human body a rigid body?
Rigid Body Dynamics. For analytical convenience, human body segments are considered as rigid bodies. A rigid body is similar to a system of particles in the sense that it is composed of particles. Therefore most of the equations for a system of particles are usable in the dynamics of a rigid body.
What is the difference between rigid body and a particle?
Basically: Particles have non-deforming mass & rigid bodies have non-deforming mass with shape & size. Rigid body analyses are required when length or size of the object much be considered, including rotation and torque.
What are the types of rigid body motion define each?
The two types of motion a rigid body can undergo are: Translational Motion. Rotational Motion.
What are the two areas of rigid body mechanics?
The mechanics of rigid bodies is sub-divided into two areas, statics and dynamics, with dynamics being further subdivided into kinematics and kinetics. Statics is the study of bodies in equilibrium.
What types of motion can a rigid body have?
The two types of motion a rigid body can undergo are: Translational Motion. Rotational Motion.
What is the importance of the dynamics of rigid bodies?
The purpose of rigid body mechanics courses is to provide engineering students with ability to analyze any problem in a simple and logical manner and to apply to its basic principles which are few and well-understood for solutions. Therefore, it has an important role in engineering education.
Is human body a rigid body?
Rigid Body Dynamics. For analytical convenience, human body segments are considered as rigid bodies. A rigid body is similar to a system of particles in the sense that it is composed of particles. Therefore most of the equations for a system of particles are usable in the dynamics of a rigid body.
What is the difference between a particle and a rigid body?
Basically: Particles have non-deforming mass & rigid bodies have non-deforming mass with shape & size. Rigid body analyses are required when length or size of the object much be considered, including rotation and torque.
What is a rigid body?
A rigid body is a collection of nodes, elements, and/or surfaces whose motion is governed by the motion of a single node, called the rigid body reference node. The relative positions of the nodes and elements that are part of the rigid body remain constant throughout a simulation. Therefore, the constituent elements do not deform but can undergo large rigid body motions. The mass and inertia of a rigid body can be calculated based on contributions from its elements or can be assigned specifically. Analytical surfaces can also be made part of the rigid body, whereas any surfaces based on the nodes or elements of a rigid body are associated automatically with the rigid body.
What are the contributions to a rigid body?
Contributions to a rigid body from mass, rotary inertia, and heat capacitance elements are accounted for automatically when these elements are connected to nodes that are part of the rigid body. A list of nodes that are part of a rigid body is generated automatically when you assign elements to a rigid body.
How to include elements in a rigid body?
To include elements in the rigid body definition, you specify the region of your model containing all of the elements that are part of the rigid body. Elements in this region or nodes connected to the elements in this region cannot be part of any other rigid body.
Why are rigid bodies useful in multibody simulations?
Although the motion of the rigid body is governed by the six degrees of freedom at the reference node, rigid bodies allow accurate representation of the geometry, mass, and rotary inertia of the rigid body .
How many degrees of freedom does a rigid body have?
Although some computational effort is required to update the motion of the nodes of the rigid body and to assemble concentrated and distributed loads, the motion of the rigid body is determined completely by a maximum of six degrees of freedom at the reference node.
What is a rigid reference node?
The rigid body reference node. A rigid body reference node has both translational and rotational degrees of freedom and must be defined for every rigid body. If the reference node has not been assigned coordinates, Abaqus will assign it the coordinates of the global origin by default.
Why is it important to make parts of a model rigid?
It may be useful to make parts of a model rigid for model verification purposes. For example, in complex models elements far away from the particular region of interest could be included as part of a rigid body, resulting in faster run times at the model development stage.
What is a Rigid Body?
A rigid body is one whose shape is precisely defined and unchangeable. It can be defined as a body where the distance between two places on the body does not change when an external force is applied.
Translational Motion of a Rigid Body
In pure translational motion, all of the body's particles have the same velocity at any one time.
Rotational Motion of a Rigid Body
When a rigid body rotates around a fixed axis, each of its particles moves in a circle that exists in a plane perpendicular to the axis and has its centre on the axis.
Translational and Rotational Equations of Motion of a Rigid Body
Rolling motion is defined as a rigid body's combination of rotational and translational motion.
Things to Remember
A rigid Body is a body whose shape doesn't change when an external force is applied to it.
Sample Questions
Ques. In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 A (1 Å = 10-10 m). Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus. (4 Marks)
Rigid Body Dynamics
The question is, what kind of motion can a rigid body have? This new outlook meant that there now could be two different types of rigid body motion. We could explore and understand more kinds of problems and in doing so develop a deeper understanding of the world around us.
Configuration Space for a Rigid Body
A macroscopic body is made up of a very large number of atoms. Describing the motion of such a system without some simplifications is clearly impossible. Many objects of interest, however, are very well approximated by the assumption that the distances between the atoms in the body are fixed.
What is every motion of a rigid body about a fixed point?
Every motion of a rigid body about a fixed point is a rotation about an axis through the fixed point.
What is the most general motion of a rigid body?
where . In words, ( 7) states that the most general motion of a rigid body is a combination of a translation and a rotation. Not surprisingly, this result was also known to Euler [ 1, 2 ]. To discuss an alternative to ( 7) that does not feature the reference configuration , we consider the motion of the body during a time interval , as illustrated in Figure 2.
What is the motion of the body at the end of the time interval?
Thus, the motion of the body at the end of the time interval is characterized by the rotation tensor that, in general, has an axis and angle of rotation that differ from those associated with . Invoking Euler’s theorem, the rotation axis of the tensor is the axis of rotation for the motion of the rigid body.
What is Figure 2?
Figure 2. Schematic of a rigid body’s initial configuration and current configuration . Also shown are the reference configuration and illustrations of the roles played by several rotation tensors in the body’s motion.
What is general motion?
A general motion of a rigid body is one in which the body may not have a fixed point. In this case, it is easy to argue that a uniform translation of the reference configuration can be imposed on the rigid body such that any one of its material points, say, , is placed at its location in the current configuration .
When was the corotational basis used?
Dating to the 18th century, the convenience of using a corotational (or body-fixed, or embedded) basis in rigid-body dynamics has been appreciated. Here, we discuss such a basis and point out some features of its use. It is of interest to note how the basis can be used to define a transparent representation for the rotation tensor of a body. Our discussion of the corotational basis follows Casey [ 4] with some minor changes.
Is a body a mass particle?
A body is considered to be a collection of material points, i.e., mass particles. Referring to Figure 1, we denote a material point of by, say, , and the vector locates the material point , relative to a fixed origin , at time .
What is rigid body dynamics?
they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. This excludes bodies that display fluid, highly elastic, and plastic behavior.
What laws describe the dynamics of a rigid body system?
This excludes bodies that display fluid, highly elastic, and plastic behavior. The dynamics of a rigid body system is described by the laws of kinematics and by the application of Newton's second law ( kinetics) or their derivative form, Lagrangian mechanics.
What is Newton's law for rigid body dynamics?
Planar rigid body dynamics. If a system of particles moves parallel to a fixed plane, the system is said to be constrained to planar movement. In this case, Newton's laws (kinetics) for a rigid system of N particles, P i, i=1,...,N, simplify because there is no movement in the k direction.
How to obtain an alternate formulation of rigid body dynamics that has a number of convenient features?
An alternate formulation of rigid body dynamics that has a number of convenient features is obtained by considering the virtual work of forces acting on a rigid body.
What is the fundamental equation that describes the behavior of a rotating solid body?
The fundamental equation describing the behavior of a rotating solid body is Euler's equation of motion :
How to determine the equations of motion of a mechanical system of rigid bodies?
The equations of motion for a mechanical system of rigid bodies can be determined using D'Alembert's form of the principle of virtual work. The principle of virtual work is used to study the static equilibrium of a system of rigid bodies, however by introducing acceleration terms in Newton's laws this approach is generalized to define dynamic equilibrium.
How many dimensions are there in orientations of rigid bodies?
Several methods to describe orientations of a rigid body in three dimensions have been developed. They are summarized in the following sections.
Why is a foundation rigid?
The foundation, in principle has to be Rigid so that the entire load of the building gets effectively transferred to the substrata. It's true that the settlement in the foundations has to be maintained within the allowable limits ( known as serviability requirements)but this is not called Flexible Foundation .
What is the difference between rigid and flexible foundations?
The main difference between rigid and flexible foundation is the rigidity of the footing.
What would happen if unsymmetrical loads were encountered?
However, if unsymmetrical loads are encountered, then a trapezoidal shape of bearing reaction would result. For flexible footings on weak and compressible soils, the bearing pressures under footing would not be linear.
What is flexible footing?
On the other hand, in flexible footing, the footing is considered to have some degree of flexibility and hence upon application of partial pressure or concentrated load the footing bends. As the footing attains the bending curvature, the soil beneath the footing base experiences non linear pressure distribution.
How is the depth of a strip foundation related to the overall width of the wall?
The depth of a strip foundation must be equal to or greater than the overall width of the wall . The width of the foundation must be three times the width of
Is a column a moment resisting frame?
Because a gravity column will likely not have significant moments, especially the interior columns of a structure. Whereas, a column which is part of a moment resisting frame will have considerable moments.
Is soil pressure uniform for rigid footing?
For rigid footing the soil pressure is not uniform but for flexible footing soil pressure is uniform.
What Is A Rigid body?
- [Click Here for Sample Questions] A rigid body is one whose shape is precisely defined and unchangeable. It can be defined as a body where the distance between two places on the body does not change when an external force is applied. In simpler language, a rigid body is one that does not modify its shape when subjected to external forces. In other ...
Rigid Body Dynamics
- [Click Here for Sample Questions] A rigid body can undergo three forms of motion: 1. Translational Motion 2. Rotational Motion 3. Combination of Translational and Rotational Motion A rigid body's motion is either pure translation or a combination of translation and rotation if it is not pivoted or anchored in some way. Rotation is the motion of a rigid body that is pivoted or fixed i…
Translational Motion of A Rigid Body
- [Click Here for Sample Questions] In pure translational motion, all of the body's particles have the same velocity at any one time. We treat the entire system as a single point-like particle with mass m at the centre of mass, travelling at the centre of mass's velocity V cm. At the centre of mass, the external force acting on the system acts Where, \(\overrightarrow{F}^{ext} = \frac{d\overrightarro…
Rotational Motion of A Rigid Body
- [Click Here for Sample Questions] When a rigid body rotates around a fixed axis, each of its particles moves in a circle that exists in a plane perpendicular to the axis and has its centre on the axis. In rotational motion, Newton's laws of motion are applied, that is, unless an external torque is given to a body, it remains in a state of rest or uniform rotational motion around a fixed axis. Ne…
Translational and Rotational Equations of Motion of A Rigid Body
- Rolling motion is defined as a rigid body's combination of rotational and translational motion. Kinetic Energy: We can get the total kinetic energy of a body by simply adding its rotational and translational kinetic energy. Thus the total kinetic energy of a particle is given by: K = \(\frac{1}{2}\)Mvcm2 + \(\frac{1}{2}\)Iω2 Where, K= Kinetic Energy of the object M= mass of the o…
Things to Remember
- A rigid Body is a body whose shape doesn't change when an external force is applied to it.
- A rigid body can undergo three forms of motion: translational motion, rotational motion and combination of translational and rotational motion.
- In pure translational motion, all of the body's particles have the same velocity at any one time.
- When a rigid body rotates around a fixed axis, each of its particles moves in a circle that exist…
- A rigid Body is a body whose shape doesn't change when an external force is applied to it.
- A rigid body can undergo three forms of motion: translational motion, rotational motion and combination of translational and rotational motion.
- In pure translational motion, all of the body's particles have the same velocity at any one time.
- When a rigid body rotates around a fixed axis, each of its particles moves in a circle that exists in a plane perpendicular to the axis and has its centre on the axis is called rotational motion of...
