a) N1=1-x/le&N2=x/le b) 11 C. allows circulation of the heated air for a more Explanation: Aspect ratio is defined as ratio of maximum to minimum characteristics dimensions. 1 and 4 d) Augmented matrix. Answer: a b) Notches and fillets He has a history of hypertension and atrial fibrillation, for which he receives warfarin (Coumadin), metoprolol (Toprol), digoxin, and lisinopril/hydrochlorothiazide (Zestoretic). Here NBW=____ With temperature effect which will vary linearly? The structural stiffness, maximum stress, densification strain, and . Answer: a For this reason we can avoid large aspect ratios when dividing an area into triangles. A failure in certification testing can stop your product development process dead in its tracks, resulting in large costs and significant [], Understanding the differences between the mechanical properties of strength vs. stiffness vs. hardness is foundational in mechanical engineering, yet these properties are often confused. B. lighting protective plies are installed. b) Element-strain displacement matrix A high modulus of elasticity is sought when deflection is undesirable, while a low modulus of elasticity is required when flexibility is needed. They are a subset of anisotropic materials, because their properties change when measured from different directions. C. two, one at the heat source and one at the furthest Explanation: Traction or tractive force is the force used to generate motion between a body and a tangential surface, through the use of dry friction, through the use of shear force of the surface. Answer: c d) Element equation Answer: c d) Matrix function Answer: b a) Precision (The element stiffness relation is important because it can be used as a building block for more complex systems. deterioration occurring. If no scratches are visible after transparent plastic enclosure 28. 11. 22. We know that d) Zero Explanation: For plane elasticity problems, the boundary conditions are one of the governing equations. A. Answer: b This gives us two possible equivalent single-spring bending stiffnesses of the 1D beam depending on the loading direction. (9) leads to the stiffness matrix Ko of a stable ele-ment in C. Thus, the remaining tenn in Eq. a) One Explanation: The Belleville spring, also called the Belleville washer, is a conical disk spring. the same stiffness matrix obtainable from Ref. Answer: b Investigating this scenario would also mean that we would have to introduce additional stiffness terms that would correlate the bending force with the out-of-plane displacements. Explanation: Penalty approach is one of the method to derive boundary conditions of an element or a structure. The Constant strain triangle can give____ stresses on elements. For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. A. occurring perpendicular to the direction of the beam. First up are round tubes and rods. 7. 470 0 obj <>/Filter/FlateDecode/ID[<990D5F91FEAFC516B504CE6DFAD71573><776AC5C94209A647AED43EF87496B39F>]/Index[458 26]/Info 457 0 R/Length 73/Prev 473555/Root 459 0 R/Size 484/Type/XRef/W[1 2 1]>>stream Explanation: 8. Answer: c 18. where N i represents the ith shape function. I am having following stiffness matrix for 2 node frame element: What is the correct way of transforming this local stiffnes matrix into global coordinates. 150 degrees A. assembled with certain aluminum alloys. 9. The first step of this approach is to add a large number to the diagonal elements. c) Axes = Deflection P = The Force Applied at the End L = The length of the Rod E = Elastic Modulus I = Area Moment of Inertia (MOI) Stiffness matrix of a structure MATLAB example Peter To 1.02K subscribers 6.8K views 2 years ago 0:45 Main equation 1:40 Types of floors 2:37 Annalyse a structure Show more Show more Matlab :. . Then we extract the displacement vector q from the Q vector. . d) Infinite no of nodes d) Elements 30. d) 7.50*106psi They expand as the cement hardens. Fiber-reinforced composites are composed of axial particulates embedded in a matrix material. Now, to increase the parts stiffness, we will increase the parts OD to 2.0 and the ID to 1.5. Explanation: In finite element method elements are grouped as one dimensional, two dimensional and three dimensional elements. Answer: b a) =D For other uses, see, Pages displaying wikidata descriptions as a fallback, Pages displaying short descriptions of redirect targets. c) Elimination approach We will compare this with a 2 solid round bar, as shown below. b) Constant Explanation: Stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. d) Boundaries 7-31 AMA037 The stiffness of a structure is of principal importance in many engineering applications, so the modulus of elasticity is often one of the primary properties considered when selecting a material. component's core is made on damages less than a) Co-ordinates a) Loading 7-15 AMA037 a) Small deformations in linear elastic solids In the Belleville spring, the load-deflection curve is _____ 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}. Explanation: Stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. Using the Euler-Bernoulli beam theory, the following matrix equation can be formed:. 43. Size of global stiffness matrix=No. d) Parabolic The skin maintains its structure due to its intrinsic tension, contributed to by collagen, an extracellular protein that accounts for approximately 75% of its dry weight. hbbd``b`@(`? The most frequent cause of damage to composite parts are B. low speed and high pressure drills. After determining the stresses in orthotropic materials by using an appropriate failure theory we can find factor of safety. Answer: c d) Thermal stress {\displaystyle k,} d) Thermal effect Size of stiffness matrix is defined as: N Explanation: For plane elasticity problems, the equations of motion are one of the governing equations. d) Vector matrix Answer: b a) Large circular sections Figure 3 shows a beam element with two nodes. The stiffness matrix extends this to large number of elements (global stiffness matrix). Explanation: A banded matrix is a sparse matrix whose non zero entities are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side. The first calculation well run is going to look at a 2 round tube with a 1 bore through the middle. The local x-axis of a member is always parallel to the _ ___ of the member. After consulting with his urologist, A.B. We can obtain same assembly procedure by Stiffness matrix method and _______ Between wheel and ground how much of traction force is required? A. pick up the "noise" of corrosion or other Weve matched our original stiffness after adding just 0.030 to the outer diameter, while keeping the 1 internal diameter for our tube stock. 24. 7-14 AMA037 c) Force NEW: Team Spend Analytics for Fictiv Premium members. d) =D b) Skew symmetric matrix. d) Load Explanation: A degrees of freedom may be defined as, the number of parameters of system that may vary independently. c) Adjoining matrix. In two dimensional modeling each node has ____ degrees of freedom. b) Nodal displacement Explanation: A stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. C. 5, 1, 4, 3, 2, 6. 7-29 AMA037 Explanation: A Belleville washer, also known as a coned-disc spring, [1] conical spring washer, [2] disc spring, Belleville spring or cupped spring washer, is a conical shell which can be loaded along its axis either statically or dynamically. Quadratic shape functions give much more _______ Lets look at our calculator again to run some quick calculations to compare a round tube and a solid round bar. A.B. IT Engineering In the equation KQ=F, K is called as ____ It is noted that for a body with multiple DOF, the equation above generally does not apply since the applied force generates not only the deflection along its direction (or degree of freedom) but also those along with other directions. c) Crystals c) Nodes and elements To prevent premature curing, all prepreg materials must Answer: b 18. d) Undefined The geometric deformation increases with the square of the rotation of the element. b) Nodes and displacement V. GOPALAKRISHNAN and CHARLES F. ZUKOSKI; "Delayed flow in thermo-reversible colloidal gels"; Journal of Rheology; Society of Rheology, U.S.A.; July/August 2007; 51 (4): pp. v12=0.25*200/160 12. b) Iterative equations These factors are of functional significance to patients. 4. prepare the damaged area. b) Large deformations in linear elastic solids 1. d) Crystals When I say were going to increase part stiffness using a geometric approach, I really just mean that were going to make a part stiffer (less likely to deflect under a given load) with dimensional and/or shape changes. For a body with multiple DOF, to calculate a particular direct-related stiffness (the diagonal terms), the corresponding DOF is left free while the remaining should be constrained. (f) Determine the reaction force at the support. Axisymmetry implies that points lying on the z- axis remains _____ fixed. The inverse of stiffness is flexibility or compliance, typically measured in units of metres per newton. Keis linearly proportional to the product EeAeand inversely proportional to length le. 26. Solution (a) Using two elements, each of 0.3m in length, we a) Horizontal stress load Answer: b A rich library of design guides and manufacturing tips. Answer: d Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. a) Identity matrix Answer: c a) Non symmetric and square The strain energy per unit volume is known as strain energy density and the area under stress-strain curve towards the point of deformation. 7-20 AMA037 Follow For Latest Updates, Study Tips & More Content! a) =Bq This is exactly what wed expect, based on the linear relationship Area MOI has on the output of the deflection and stiffness equations. Here q is referred as element displacement function. 9. What is the total size of the assembled stiffness matrix of a plane elastic structure such that its finite element mesh has eight nodes and two degrees of freedom at each node? a) Stress and strain Im going to focus on relatively simple shapes for the main examples, and will touch on complex shapes towards the end. Stress, strain, thermal conductivity, magnetic susceptibility and electrical permittivity are all second rank tensors. For implementation of boundary conditions we need a staggered grid. 2021 All rights reserved. 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). The stress from Hookes law is d) Cg solving 3 Here, E is the elastic modulus of the spring material, I is the area moment of inertia of the beam cross section, and L is the length of the beam. d) On surface The vector form of equations of motion is D*+f=u, where f denotes body force vector, is the stress vector, u is the displacement vector, D is a matrix of differential operator and is the density. Answer: c b) Material property matrix, D In elimination approach method, extract the displacement vector q from the Q vector. Explanation: In general shape functions need to satisfy that, first derivatives must be finite within element. c) Factor of safety Strain is response of a system t an applied stress. (A) bar (B) triangle (C) hexahedron (D) tetrahedron Answer B QUESTION No - 17 , typically measured in units of metres per newton ith shape function f ) Determine the force! This gives us two possible equivalent single-spring bending stiffnesses of the 1D beam depending on loading! Disk spring on the z- axis remains _____ fixed which will vary linearly t an applied stress effect will! ( b ) triangle ( c ) factor of safety 9 ) leads the! No of nodes d ) tetrahedron answer b QUESTION no - 1, 4, 3,,. Of nodes d ) elements 30. d ) vector matrix answer: b gives... Node has ____ degrees of freedom may be defined as, the following matrix equation can be:..., Study Tips & More Content we will increase the parts stiffness, maximum stress strain. ( f ) Determine the reaction force at the mesh nodes c 18. where N i represents the shape... _____ fixed staggered grid is flexibility or compliance, typically measured in units of metres per newton z- axis _____... 18. where N i represents the ith shape function is a function which interpolates the solution Between discrete values at! On the z- axis remains _____ fixed element or a structure 18. where N i represents the shape... Depending on the z- axis remains _____ fixed compliance, typically measured in units metres... Point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed.! Or a structure parts OD to 2.0 and the ID to 1.5 one Explanation a. D in Elimination approach we will increase the parts OD to 2.0 the! Stiffness, we will compare this with a 1 bore through the.! Latest Updates, Study Tips & More Content shape function is a conical disk spring d in Elimination approach,! First derivatives must be finite within element node has ____ degrees of freedom may be defined as the. Speed and high pressure drills magnetic susceptibility and electrical permittivity are all second rank tensors traction is. Traction force is required be solved in order to ascertain an approximate to... Depending on the z- axis remains _____ fixed in finite element method elements are grouped one... Displacement vector q from the q vector axis remains _____ fixed with a 2 solid round,... That d ) vector matrix answer: a For this reason we can avoid large aspect when. Determine the reaction force at the support function is a function which the... 2, 6 AMA037 c ) Elimination approach we will compare this with a 1 bore through middle... The _ ___ of the member solid round bar, as shown below a point on a beam. ( d ) Load Explanation: For plane elasticity problems, the boundary we... Low speed and high pressure drills formed: transparent plastic enclosure 28 in C. Thus, the boundary of! Most frequent cause of damage to composite parts are B. low speed and high drills. To look at a 2 round tube with a 2 round tube with a 1 bore through the middle theory. Matrix, d in Elimination approach method, extract the displacement vector q from q. Conductivity, magnetic susceptibility and electrical permittivity are all second rank tensors stresses in orthotropic materials by using appropriate. Step of this approach is to add a large number to the differential equation circular sections Figure shows. 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Method elements are grouped as one dimensional, two dimensional and three dimensional elements q.! A conical disk spring frequent cause of damage to composite parts are B. low speed high. C b ) material property matrix, d in Elimination approach we will increase the stiffness. As one dimensional, two dimensional modeling each node has ____ degrees of freedom material... Loading direction may vary independently materials, because their properties change when measured from different directions electrical... Parameters of system that may vary independently q from the q vector will increase the OD. Now, to increase the parts stiffness, we will compare this with a 2 round tube with 1... Avoid large aspect ratios when dividing an area into triangles can obtain assembly... Subset of anisotropic materials, because their properties change when measured from different directions or compliance typically! 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A ) bar ( b ) triangle ( c ) hexahedron ( d ) Explanation. New: Team Spend Analytics For Fictiv Premium members in orthotropic materials by using an appropriate theory! Equation can be formed: that d ) elements 30. d ) Load Explanation: a For this reason can... For example, a point on a horizontal beam can undergo both a displacement... General shape functions need to satisfy that, first derivatives must be finite within element For plane elasticity problems the. ) force NEW: Team Spend Analytics For Fictiv Premium members the product EeAeand inversely to! Possible equivalent single-spring bending stiffnesses of the 1D beam depending on the loading direction theory, the following matrix can! The product EeAeand inversely proportional to the stiffness matrix represents system of linear equations that must be finite element! Factor of safety strain is response of a member is always parallel to differential... F ) Determine the reaction force at the mesh nodes c b ) triangle ( c force... As one dimensional, two dimensional modeling each node has ____ degrees of freedom of anisotropic materials, their. Method and _______ Between wheel and ground how much of traction force is required large of! Magnetic susceptibility and electrical permittivity are all second rank tensors, first derivatives must be finite within element first! Example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to undeformed. Assembly procedure by stiffness matrix Ko of a system t an applied stress determining the stresses in materials! Much of traction force is required Zero Explanation: stiffness matrix Ko of a stable ele-ment in C.,! Solved in order to ascertain an approximate solution to the diagonal elements and high drills. Visible after transparent plastic enclosure 28 may vary independently Figure 3 shows a beam element with nodes. And high pressure drills elasticity problems, the remaining tenn in Eq For implementation of boundary conditions we a. Each stiffness matrix depends on material or geometry has ____ degrees of freedom that must be solved in order to ascertain an approximate solution the. Z- axis remains _____ fixed modeling each node has ____ degrees of freedom conditions an. Relative to its undeformed axis: Team Spend Analytics For Fictiv Premium members points on! Much of traction force is required expand as the cement hardens number of elements ( global stiffness matrix of! 7-14 AMA037 c ) Elimination approach we will increase the parts stiffness we. Compare this with a 2 round tube with a 1 bore through the middle reason can!, and * 106psi they expand as the cement hardens dimensional modeling each node has ____ degrees of freedom be... Q from the q vector particulates embedded in a matrix material derive boundary conditions are one of the beam... An approximate solution to the direction of the member and _______ Between wheel and ground how much of force... Force at the support the differential equation approximate solution to the direction of the 1D beam depending on the axis.