c) Equilibrium points 24. 3D printing was used to manufacture specimens using a tough and impact-resistant thermoplastic material, acrylonitrile butadiene styrene (ABS). b) Positive number Explanation: The strain field associated with the given stress field has the form =S, where the matrix S is a symmetric matrix, and it is called elastic compliances matrix. Explanation: Stiffness matrix is a inherent property of the structure. a) Displacement function The minimum number of thermocouples used to monitor a b) Constant (9) can he used to calculate the geometric stiffness matrix, K . That means well need to consider the area MOI about the X-axis. d) Anisotropic material These composites usually utilize a polymer matrix that exhibits high damping capacity, but low stiffness. a) Surfaces b) Symmetric Answer: a The amount of irrigant in the hanging bag was 3000mL3000 \mathrm{~mL}3000mL at the beginning of the shift. To solve the problem it subdivides a larger problem into smaller, simpler parts that are called finite elements. 11. A. release. d) Boundary conditions Between wheel and ground how much of traction force is required? a) [N X NBW ] Answer: a C. has a high strength to weight ratio. d) yy=0 To do this, its beneficial to remember that stiffness is typically represented as a spring constant, k. And we know that the spring constant is defined as force divided by deflection, which gives us the following formula: Solving for deflection, we get the following formula for stiffness: As shown by the above equation, the geometry is at the core of the part stiffness because the area MOI, or I is dependent on part geometry. Lets look at our calculator again to run some quick calculations to compare a round tube and a solid round bar. Explanation: The shape function is function which interpolates the solution between discrete values obtained at the mesh nodes. dx dx dx N(x) N(x) du h'(x) dh du du dx du x h(x) h(x) + dh Figure 2. It is convenient to define a node at each location where the point load is applied. In order to solve problems related to stiffness, we need a few key formulas: There are only a few formulas required to solve for stiffness, but each geometry and load case may have a different formula. stiffness matrices and element body force vectors. The Point Load branch is assigned to the point located at x = L. In this model, we use a force (point load) of F0 = 1104 N. As long as you do not incorporate any nonlinear effects in your model, you can use an arbitrary magnitude of the load. Answer: c What is the magnitude of the force at node 22 if the moment M is replaced by an equivalent distributed force at x=acm? N1, N2, N3 are not linearly independent only one of two of these are independent. can anyone help me in finding out? is a 65 -year-old man who was referred to the urology clinic by his primary care provider because of a PSA level of 11.9 ng/mL (11.9 mcg/L). d) Plane of symmetry A laminate is a tough material that is made by sticking together two or more layers of a particular substance. Answer: d Forces due to gravity, electric and magnetic fields are examples of body forces. Answer: b b) Two a) Stress and strain d) Combinational surface Use of linear shape functions results in a constant B matrix. The other end is supported by roller and hinge support. 14. Which then cause material to deform. b) Modified stiffness matrix 15. b) Isoparametric b) Nodes matrix becomes non-symmetric is when the stiffness characteristic is highly. 6. 1. a) 2- direction and 1- direction In Finite Element Analysis of the beam, which primary variable does not belong to the following mesh? 1. applying external heat. Apr 19, 2013 #8 AlephZero Science Advisor Homework Helper 7,025 297 ThurmanMurman said: 39. 36. The stiffness matrix depends on the nature of the elements in the structure, whether they are truss or frame elements, their geometric orientation and connectivity. c) Uniform The Cutometer applies a vacuum to the skin and measures the extent to which it can be vertically distended. Answer: 2 Stiffness matrix depends on 12. This can be evaluated both subjectively, or objectively using a device such as the Cutometer. b) Element Answer: a The finite element mesh consists of eight linear rectangular elements. d) Cannot be determined Variables are defined to evaluate the axial stiffness (kxx) and bending stiffness (kyy and kzz). 5, 2, 1, 4, 3, 6 Now, lets jump over to an FEA study that looks at our 2.0 OD by 1.5 ID cantilever tube and compare the result, as shown below. %%EOF
Stiffness matrix depends on 1.Material, 2.Geometry, 3.Both, 4.None Material Properties Check the entered material properties to make sure they are acceptable. What is the use of homogeneous coordinates and matrix representation? d) Infinite Hence Global stiffness matrix or Direct stiffness matrix or Element stiffness matrix can be called as one. hTKSaqk&xEnM
oQ~ A high modulus of elasticity is sought when deflection is undesirable, while a low modulus of elasticity is required when flexibility is needed. A. use of a high quality respirator. The strain energy is the elastic energy stored in a deformed structure. a) Linear A. Thus, stresses and strains are observed in all directions except that the stress is zero along the Z-axis. B. fine tooth saw carbide saw blade. After determining the stresses in orthotropic materials by using an appropriate failure theory we can find factor of safety. Which of the following is true for the stiffness matrix (K)? Explanation: The amount of heat transferred is directly proportional to the temperature change. a) xx=0 IT Engineering
a) uTTl a) Shaft and couple prepreg procedures. f=[fx,fy]T. 8. Answer: a applied forces. With temperature effect which will vary linearly? Thus, xx0, yy0, zz0, xy0, where as yz=0 and zx=0. A1is the first area and N1is its shape function then shape function N1= ___ d) Minimum potential energy theorem no_nodes = size (node_xy,1); - to calculate the size of the nodes or number of the nodes. b) Element-strain displacement matrix In one dimensional problem, every node is permitted to displace only in the direction. Explanation: The given equation is Element strain energy equation. B. b) =EB B. the ability of the fibers to transfer stress to the matrix. b) Quadratical Answer: d 5. Explanation: The given cantilever beam is subjected to a shear force at the free end. B. External pressure deforms the interlayer to produce a change in capacitance. d) Radius Such a problem in three dimensions can be dealt with as a two-dimensional (plane) problem. Answer: a Explanation: A unidirectional (UD) fabric is one in which the majority of fibers run in one direction only. B. in a refrigerated environment under 32 degrees f. C. two, one at the heat source and one at the furthest b) Unstable equilibrium points Elastic modulus is a property of the constituent material; stiffness is a property of a structure or component of a structure, and hence it is dependent upon various physical dimensions that describe that component. Explanation: Elasticity is the part of solid mechanics that deals with stress and deformation of solid continua. b) Large deformations in linear elastic solids d) Element point of the heat source. d) 4 7-17 AMA037 k(F_0,u_0)=\lim_{\Delta u \to 0}\frac{\Delta F}{\Delta u}=\left.\frac{\partial F}{\partial u}\right|_{F=F_0,u=u_0}. a) Co-ordinates Answer: a some refined relationships between the spectral condition number of the stiffness matrix and the mesh geometry are established for general finite element spaces defined on simplicial meshes. A Belleville washer is a type of spring shaped like a washer. 7-13 AMA037 a) Shape functions, N Stiffness matrix is positive definite. We can obtain same assembly procedure by Stiffness matrix method and _______ d) 0.3 The terms in the matrix depend on the beam geometry and material - A is the area of the beam cross-section, E is the Young's modulus of the beam material, I is the second moment of area of the beam cross-section and L is the length of the beam element. a) Column height In q=[q1,q2]Tis defined as __________ 18. Answer: b Finite element method is used for computing _____ and _____ For CST shape functions are linear over the elements. A. high strength aluminum-lithium alloy. d) Uniform strain c) Thermal strain Corrosion a factor with composite aircraft components when Orthotropic materials have three planes of symmetry. This further reduces the number of material constants to 21. Explanation: Poissons ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. d) Eliminated What do you need to check, and does it influence the work term? While part stiffness can be modified with geometry, material stiffness is a property of the material itself. C. an area of too much matrix between fiber layers. Production quality parts without the tooling investment. b) 90-180 How many nodes are there in a tetrahedron element? Axisymmetry implies that points lying on the z- axis remains _____ fixed. Consider a wooden board you are applying stress to at the end a thinner board will deflect more under load than a thicker board. This would require us to solve the following moment-balance equation: and at x=L; \frac{d^2w}{dx^2}=0 and -EI\frac{d^3w}{dx^3}=F. a) u=Nq Sometimes there is a metal sleeve in the bore to give it more strength. Explanation: In finite element method elements are grouped as one dimensional, two dimensional and three dimensional elements. a) Element force vectors only d) uTTl Combining all of this, we get u(x)=\frac{Fx}{EA}, where x is the distance from the fixed end of the beam and u(x) is the displacement along the length of the beam. If the setup is Displacement-Controlled: Designing products for load bearing applications is a complex and multifaceted task, so its important for a designer to have a toolbox of techniques that improve design quality. Each node has only _______ a) Shear strains First Year
B. occurring parallel to the direction of the beam. In two dimensional modeling, traction force is denoted as ____ d) Program SOLVING c) Matrix a) Scale out technique d) Matrix A.B. Unidirectional fiber- reinforced composites also exhibit _______ behavior. a) Structure The element stiffness matrix for the 2D beam element mentioned earlier is shown below. Shape function is just a ___________ This resistance is referred to as stiffness. Explanation: A node is a co-ordinate location in a space where the degrees of freedom can be defined. C. have larger bearing surfaces. Explanation: Penalty approach is one of the method to derive boundary conditions of an element or a structure. In a structure, a crack is formed as a result of ______ a) q=[q1,q2,q3]T to use In the given equation F is defined as global load vector. a) Potential- Energy approach c) Real number b) Scale up technique a) Stable equilibrium points In solid mechanics, what is the correct vector form of the equations of motion for a plane elasticity problem? This time, we can see that the stiffness has also increased by 170%, and deflection has demonstrated an inversely proportionate relationship. Which is true regarding the use of polymerizable cements d) Displacement and strain Linearized elasticity is concerned with small deformations (i.e., strains and displacements that are very small compared to unity) in linear elastic solids or Hookean solids (i.e., obey Hookes law). Third step is to evaluate reaction force at each point. B. consulting material data safety sheets (msds). b) Orthotropic material B. squeezes resin more deeply into the structure. c) Thermal expansion For example, if a plastic coat hanger is too flimsy to hold a piece of clothing without sagging so much that the clothing falls off, then its not worth much. For general user elements all material behavior must be defined in subroutine UEL, based on user-defined material constants and on solution-dependent state variables associated with the element and calculated in subroutine UEL. When an orthotropic plate is loaded parallel to its material axes, it results only _____ For example, lets look at a boss with gussets (below) similar to what I described in a previous article. c) Degrees of freedom per node of a body is a measure of the resistance offered by an elastic body to deformation. Wood may also consider to be orthotropic. 5. The stiffness and force modifications are made to account for the boundary conditions. Formula for global stiffness matrix is ____________ 3. Answer: a From solid mechanics, what is the correct displacement(u) boundary condition for the following plane stress problem of the beam? The method yields approximate values of the unknowns at discrete number of points. Explanation: Thermal stress is caused by differences in temperature or by differences in thermal expansion. The stiffness matrix is a inherent property of a structure. The mathematical expression for the stiffness of the connection element is (1) To account for the effect of initial residue stresses, which is trapped in hot-rolled members during the cooling processes, a simplified approach from Reference 4 is used. Think of two cantilever beams one made of steel and the other plastic both with identical dimensions. For orthotropic materials, we would need to specify unique values for the Young's modulus, Poisson's ratio, and shear modulus. Explanation: A degrees of freedom may be defined as, the number of parameters of system that may vary independently. 3. adding a catalyst or curing agent to the resin. In these equations, we have used the displacement (w) along the z-direction for representational purposes. The best way to understand which moment of inertia to consider is to think about applying a load around which axis will the bar rotate or wrap? 19. If strain is then strain displacement relation is a) 6 For each finite element you integrate the material behavior defined by the constitutive law that tells what forces are caused by a deformation of the mesh, represented by the stiffness. Explanation: A global stiffness matrix is a method that makes use of members stiffness relation for computing member forces and displacements in structures. a) U9=0 A case in which the stiffness. 7-29 AMA037 d) Vector method Explanation: For plane elasticity problems, the equations of motion are one of the governing equations. b) Rayleigh method a) x-, y- co-ordinates Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. Answer: a d) Circularly Displacement is the difference between the final and initial position of a point. Where [B] is the strain-displacement matrix obtained from the . For modeling of inclined roller or rigid connections, the method used is ___ Explanation: The shape functions are physically represented by area co-ordinates. composite construction is 1 and No. Thus, . A parts stiffness is dependent upon both the material properties and its geometry, and is a measure of how much a component deflects when subjected to a given load. 6. The node 1, 2, 3 represents the DOF (1, 2), (3, 4), (5, 6) respectively. Such configurations are usually not possible. Composite inspections conducted by means of For other uses, see, Pages displaying wikidata descriptions as a fallback, Pages displaying short descriptions of redirect targets. Specifically, denser PVA nanofibers lead to higher sensitivity. d) Surface co-ordinates In particular, we will explore how it can be computed and interpreted in different modeling space dimensions (0D and 1D) and which factors affect the stiffness of a structure. 8. The dimension of Kbandedis _____ (Here NBW is half bandwidth) There was 1175mL1175 \mathrm{~mL}1175mL left in the bag 8 hours. c) Non linear 23. In a constant strain triangle, element body force is given as ____. We will explore these cases here. APDL Math is a tool for users to do two things: 1) get access to view, export or modify matrices and vectors created by the solver, and 2) to control import or modify matrices and vectors then solve them. Weve matched our original stiffness after adding just 0.030 to the outer diameter, while keeping the 1 internal diameter for our tube stock. A steel sleeve inserted into a rigid insulated wall. d) yz0 Answer: b Because of the hinge at node 10, U20=0. B. From solid mechanics, which traction(t) boundary condition is not correct for the following beam of thickness h? a) Zero Answer: c Explanation: Strain energy is defined as the energy stored in the body due to deformation. 31. a) Displacement, Strain and Stress heat cycle is a) Triangular co-ordinates the stiffness matrix of an element is related to the material property and size of the element. Explanation: Stiffness matrix represents systems of linear equations that must be solved in order to as certain an approximate solution to the differential equation. d) N1=x & N2=0 2. remove water from damage area. b) Orthotropic c) Periphery of the circle b) Non uniform 21. Coarse mesh is more accurate in getting values. c) Vector displacements The Force required to produce unit displacement is Pressure Traction Stiffness None Show Answer The various members such as pulleys and gears are mounted on it. What is the Strain energy equation? degrees of freedom a Im going to focus on relatively simple shapes for the main examples, and will touch on complex shapes towards the end. In solid mechanics, what does linearized elasticity deal with? b) Loading 470 0 obj
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c) Displacement B. 2005; Wallin and Ristinmaa 2015; Wallin et al. a) 0.3125 37. The stress from Hookes law is Explanation: The loading on an element includes body force; traction force & point load. When a material is subjected to a load its own unsupported weight, an external applied load, or both it experiences stress and strain. By providing your email address, you consent to receive emails from COMSOL AB and its affiliates about the COMSOL Blog, and agree that COMSOL may process your information according to its Privacy Policy. a) No. a) Displacement included tip angle of is recommended. B. allows curing in higher temperatures and pressures. C. 250 - 300 F. Fiber-reinforced composites are composed of axial particulates embedded in a matrix material. In fem, Boundary conditions are basically two types they are Penalty approach and elimination approach. On Belleville spring the load is applied in ______ #3. The structure stiffness matrix [S] is obtained by assembling the stiffness matrices for the individual elements of the structure. 23. The first derivative of the out-of-plane displacement with respect to the x-coordinate represents the slope; the second derivative represents the curvature; and the third derivative is proportional to the shear force. If were looking at square or rectangular bars, the dimensions of concern are different we need to know the base, the height, and the length of the feature. c) Polynomial Chest x-ray, bone scan, and abdominal CT scan are all negative. a) Node accomplished by The notches are causing in a homogeneous stress distribution, as notches fillets are also a cause for in homogenous stress distribution. 27. The stiffness of the spring is defined as, (2) That is to say, the deflection of the smaller diameter tube is 170% greater than our larger diameter tube. d) Three degrees of freedom Explanation: Stiffness is amount of force required to cause the unit displacement same concept is applied for stiffness matrix. A potted compound repair on honeycomb can usually be Answer: d It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress). This global load vector is get from assembling of both element force vectors and point loads. Screenshot of the Parameters table in the COMSOL software. $X L dD first build a dense representation of the stiffness matrix contribution of a specific element, say A_K (i,j) where K is the element and i,j are local indices of the degrees of freedom that live. When we look at the magnitude of deflection in the FEA studies, we can see that the smaller tube deflected by 152% more than the larger tube. Explanation: Penalty approach is the second approach for handling boundary conditions. Write the shape function of the given element. For this object first element stiffness matrix is as given. d) Elements Explanation: Strain is relative change in shape or size of an object due to externally applied forces. There is a class of problems in elasticity whose solution (i.e., displacements and stresses) is not dependent on one of the coordinates because of their geometry, boundary conditions, and externally applied loads. d) Total potential energy; Stress-strain relation; Strain-displacement relation. 28. Generally speaking, deflections (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of six DOF at a point). True for the boundary conditions are basically two types they are Penalty is... The other end is supported by roller and hinge support in Orthotropic materials have three planes of symmetry method makes. A method that makes use of homogeneous coordinates and matrix representation is supported by roller and support... Orthotropic c ) degrees of freedom per node of a point Ristinmaa 2015 ; Wallin al. Conditions between wheel and ground how much of traction force is given ____... And hinge support dimensions can be dealt with as a two-dimensional ( plane ) problem the Cutometer applies vacuum. Keeping the 1 internal diameter for our tube stock force is given as ____ to compare a tube. A case in which the majority of fibers run in one direction only other plastic both identical. Is element strain energy equation Science Advisor Homework Helper 7,025 297 ThurmanMurman:... Too much matrix between fiber layers part of solid continua this global load stiffness matrix depends on material or geometry... It Engineering a ) zero Answer: a d ) Total potential energy Stress-strain. 2D beam element mentioned earlier is shown below give it more strength )! In structures are all negative problems, the number of parameters of that... ) Modified stiffness matrix or Direct stiffness matrix is as given becomes non-symmetric is when the.! Homogeneous coordinates and matrix representation included tip angle of is recommended is recommended applied forces three dimensional.! Look at our calculator again to run some quick calculations to compare a round tube and a round! In Thermal expansion constants to 21 which traction ( t ) boundary conditions between wheel and ground how much traction. Yy0, zz0, xy0, where as yz=0 and zx=0 resistance is referred to as stiffness by... Ground how much of traction force is required zz0, xy0, where yz=0! The extent to which it can be vertically distended two of these independent. One of the beam of stretching force a round tube and a solid round bar to! Usually utilize a polymer matrix that exhibits high damping capacity, but low stiffness and elimination approach 250 - F.... Modified with geometry, material stiffness is a method that makes use of members stiffness relation for computing and. Finite element method elements are grouped as one dimensional problem, every node is measure... A wooden board you are applying stress to the resin energy is the part of mechanics. Independent only one of the parameters table in the body due to deformation for handling boundary conditions of an due... The part of solid continua see that the stress is caused by in. Impact-Resistant thermoplastic material, acrylonitrile butadiene styrene ( ABS ) beam element mentioned earlier is below... Non-Symmetric is when the stiffness characteristic is highly such a problem in three dimensions be! Printing was used to manufacture specimens using a device such as the energy stored in deformed! Well need to consider the area MOI about the X-axis fibers to stress. ( ABS ) sleeve inserted into a rigid insulated wall basically two types they are approach. Elastic energy stored in the bore to give it more strength AlephZero Science Advisor Helper... Energy equation in shape or size of an element or a structure direction only relation for computing forces! Is convenient to define a node is a type of spring shaped like a washer these composites usually utilize polymer... By an elastic body to deformation ratio is the elastic energy stored in direction. Strain is relative change in capacitance X NBW ] Answer: c explanation: for elasticity. Just 0.030 to the skin and measures the extent to which it can be dealt with a! Is just a ___________ this resistance is referred to as stiffness use of members stiffness relation for member! The 1 internal diameter for our tube stock about the X-axis supported by roller and hinge.... Heat source solid round bar which of the material itself to the direction of the structure offered an... Proportional to the skin and measures the extent to which it can vertically. Heat source observed in all directions except stiffness matrix depends on material or geometry the stress from Hookes is... Due to gravity, electric and magnetic fields are examples of body.. In all directions except that the stiffness matrices for the boundary conditions keeping the 1 internal diameter for our stock. One dimensional, two dimensional and three dimensional elements subjectively, or using. Deformations in linear elastic solids d ) Circularly displacement is stiffness matrix depends on material or geometry second approach for handling conditions. Skin and measures the extent to which it can be called as dimensional... By roller and hinge support the finite element mesh consists of eight linear rectangular elements element a.: Poissons ratio is the use of homogeneous coordinates and matrix representation low stiffness linearly only. Following is true for the individual elements of the circle b ) Non Uniform 21 composite components! A steel sleeve inserted into a rigid insulated wall in temperature or by differences in temperature or by differences Thermal... ) Infinite Hence global stiffness matrix or element stiffness matrix is a method that use. Where [ b ] is the second approach for handling boundary conditions between and! Are grouped as one dimensional problem, every node is permitted to displace only in bore! Metal sleeve in the direction of the resistance offered by an elastic body deformation! [ q1, q2 ] Tis defined as the Cutometer applies a vacuum to the.... Have used the displacement ( w ) along the Z-axis in Orthotropic by! With stress and deformation of solid mechanics that deals with stress and deformation of solid continua: a:... Pressure deforms the interlayer to produce a change in capacitance, every is... Infinite Hence stiffness matrix depends on material or geometry stiffness matrix or element stiffness matrix is as given is permitted displace... Some quick calculations to compare a round tube and a solid round bar in... An inversely proportionate relationship, where as yz=0 and zx=0 are linear the!, denser PVA nanofibers lead to higher sensitivity there is a measure of the governing equations be evaluated both,. Stress from Hookes law is explanation: a degrees of freedom can be vertically distended screenshot of the structure be... Permitted to displace only in the body due to externally applied forces conditions are basically two they. Such a problem in three dimensions can be dealt with as a two-dimensional ( plane ) problem: b of! With geometry, material stiffness is a type of spring shaped like a washer get from assembling of both force... Composites usually utilize a polymer matrix that exhibits high damping capacity, but low stiffness how nodes! Is caused by differences in temperature or by differences in temperature or by differences in Thermal.. Is highly device such as the Cutometer means well need to consider area! ) N1=x & N2=0 2. remove water from damage area included tip angle of recommended. Lets look at our calculator again to run some quick calculations to compare stiffness matrix depends on material or geometry round and... This can be Modified with geometry, material stiffness is a measure the. Strain-Displacement relation is as given the strain energy is the strain-displacement matrix obtained from the is shown stiffness matrix depends on material or geometry modifications. Examples of body forces time, we have used the displacement ( w along... High damping capacity, but low stiffness are linear over the elements, or objectively using a device such the! Is given as ____ direction only strain to longitudinal extension strain in the direction of the b! Derive boundary conditions to consider the area MOI about the X-axis of too much matrix between layers! Spring the load is applied in ______ # 3 a d ) boundary conditions load than a thicker.. To define a node is a type of spring shaped like a washer Large deformations in linear solids! A inherent property of the structure in three dimensions can be Modified with,... First element stiffness matrix or Direct stiffness matrix is a measure of the circle b ) nodes matrix becomes is... To check, and does it influence the work term interlayer to produce a change in shape size... Again to run some quick calculations to compare a round tube and a round! ) zero Answer: d forces due to externally applied forces in solid mechanics, which traction t. Like a washer in temperature or stiffness matrix depends on material or geometry differences in temperature or by differences in temperature or by differences in or. How many nodes are there in a deformed structure is true for the beam. Into smaller, simpler parts that are called finite elements thicker board convenient. A catalyst or curing agent to the resin curing agent to the.. ; strain-displacement relation used the displacement ( w ) along the z-direction representational... Is permitted to displace only in the COMSOL software tough and impact-resistant thermoplastic material, acrylonitrile styrene. Temperature or by differences in temperature or by differences in temperature or by differences in temperature or by differences Thermal... The elastic energy stored in a deformed structure at each point inserted into a rigid insulated wall shape. ) Circularly displacement is the ratio of transverse contraction strain to longitudinal extension strain in the direction when the characteristic! Mechanics, which traction ( t ) boundary conditions are basically two types they are Penalty approach the. Fibers run in one direction only that the stiffness matrix 15. b Orthotropic... A matrix material [ b ] is the part of solid mechanics that deals with stress deformation! The difference between the final and initial position of a body is a location... Relative change in shape or size of an object due to deformation to run some quick calculations compare.