B. are more electrically conductive to aid in You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Keep production lines running without the excess inventory. Answer: b Since the translation along x is constrained, U9=U19=U29=0. a) Isotropic Stresses due to rigid body motion are _______________ Explanation: A body force is a force that acts throughout the volume of the body. Explanation: Local coordinate system corresponds to particular element in the body. In finite element modeling every element connects to _______ A. water from between the laminations. They are a subset of anisotropic materials, because their properties change when measured from different directions. b) Vigorously Answer: d Explanation: The given cantilever beam is subjected to a shear force at the free end, thus tx(0, y)=0 and ty(0, y)=-hT. The stiffness matrix is a inherent property of a structure. 7-41 AMA078 eliminate corrosion. d) No traction force a) Entire body 1. d) N3=1-- 7-31 AMA037 d) 1 degree of freedom Answer: a C. poor formability. 11. Specifically, it measures the fractional change in size per degree change in temperature at constant pressure. 14. E1value of Balsa wood is ___ As node 22 is located at the center, it is neither pushed nor pulled; thus, the effective force at node 22 is always zero. Common problems are as follows: Poisson's Ratio of 0.5. C. in corners and around the edges of the structure. d) T Others.. The element stiffness matrix is zero for most values of iand j, for which the corresponding basis functions are zero within Tk. Which is not a characteristic of acrylic plastics Explanation: Strain is defined as a geometrical measure of deformation representing the relative displacement between particles in a material body. For the special case of unconstrained uniaxial tension or compression, Young's modulus can be thought of as a measure of the stiffness of a structure. Stiffness matrix is a a) Symmetric matrix. b) Deformation b) Potential energy Body force is distributed force acting on every elemental volume. a) Stress-strain relation high strength and high elastic modulus for its weight.) I suggest you to refer the following book: The Finite Element Method Using MATLAM : Hyochoong Bang (Author), Young W. Kwon (Author) Refer the book..Book discusses basics of FEM with MATLAB Code. b) Natural boundary condition When it comes to calculating the area MOI for a tube, the only dimensions we will need are the Outer Diameter (OD) and Inner Diameter (ID). a) Row vector Answer: a W;>5/)b36dsC 0=Lq'wulXccCnp|_%3MF@X2qiU8Dscckxm=^e2` 2. remove water from damage area. d) Singular matrix a) Infinite Crack propagation problems come under this category. The distribution of change in temperature, the strain due to this change is initial strain. Between wheel and ground how much of traction force is required? b) One degree of freedom Stiffness matrices are square and symmetric. 28. to use In finite strain stiffness optimization, several potential definitions of the structural stiffness are available, such as structural strain energy, end displacement, end compliance, and end stiffness (Kemmler et al. Answer: b d) The initial displacement and final velocity 13. d) A1 On gathering stiffness and loads, the system of equations is given by. c) Elements study. Explanation: Aspect ratio is defined as ratio of maximum to minimum characteristics dimensions. I have a question. That is, all the elements outside the band are zero. b) Nodes and displacement Apr 19, 2013 #8 AlephZero Science Advisor Homework Helper 7,025 297 ThurmanMurman said: Finite element method is used for computing _____ and _____ Explanation: From nodal displacement equation we can write that isoparametric equation as Stiffness matrix is _____ d) yy=0 The objective of fiber-reinforced composites it to obtain a material with high specific strength and high specific modulus. 4. 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. b) Z direction Explanation: To calculate the magnitude, assume that the force causing the moment is linear with y. In particular, N1+N2+N3represent a plane at a height of one at nodes ______ c) Adjoining matrix. Explanation: If an external force acts to give the particles of the system some small initial velocity and kinetic energy will developed in that body then the point where kinetic energy decreased that point is Stable equilibrium point and the point where the kinetic energy dramatically increased then the point is called Unstable equilibrium points. Explanation: The co-efficient of thermal expansion describes how the size of an object changes with a change in temperature. Answer: d Accelerating new product introduction for the robotics industry, Accelerating new product introduction for the consumer products industry, Accelerating new product introduction for the medical industry, Accelerating new product introduction for the automotive industry, Accelerating new product introduction for the aerospace industry. Look at earlier problem and plot the PvP-vPv diagram for the process. Let's take a typical and simple geometry shape. 19. Third step is to evaluate reaction force at each point. B. 7-30 AMA037 This global load vector is get from assembling of both element force vectors and point loads. The shape functions are physically represented by _____ b) Scale up technique d) Vector method of nodes*Degrees of freedom per node. 23. The stiffness is a one of the key measures in. Explanation: Deformation changes in an objects shape or form due to the application of a force or forces. Stiffness matrix depends on (A) material (B) geometry (C) both material and geometry (D) none of the above Answer C QUESTION No - 16 Example of 2-D Element is ___________ . C. allows circulation of the heated air for a more External pressure deforms the interlayer to produce a change in capacitance. An element is a mathematical relation that defines how the degrees of freedom of a node relate to next. Answer: a This may be as simple as increasing the diameter of a rod or as complex as adding gussets to certain bosses. Answer: b c) Transverse axis. The geometry has been discretized as shown in Figure 1. the same stiffness matrix obtainable from Ref. 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. Answer: a 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. B. Explanation: 8. / Answer: b Answer: a Essentially, the factor of safety is how much stronger the system is than it needs to be for an intended load. b) Virtual work energy 22. b) =du/d What is a shape function? surface or through the plastic, the plastic is said to be He has discussed his diagnosis with the urologist. c) Total potential energy For a plane strain problem, which strain value is correct if the problem is characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0? b) -,-Co-ordinates Today, we will introduce the concept of structural stiffness and find out how we can compute the stiffness of a linear elastic structure subjected only to mechanical loading. Global nodes corresponds to _______ 28. The Dzhanibekov Effect Explained. FEM basis is in the stiffness matrix method for structural analysis where each element has a stiffness associated with it. d) Load %PDF-1.5 % Further measures of stiffness are derived on a similar basis, including: The elastic modulus of a material is not the same as the stiffness of a component made from that material. [k] is the structure stiffness matrix that relates the two vectors. Explanation: The plane strain problems are characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0, where (ux, uy, uz) denote the components of this displacement vector u in the (x, y, z) coordinate system. b) Two Explanation: A constant strain element is used to provide an approximate solution to the 2D domain to the exact solution of the given differential equation. View Answer 3. Only No. Explanation: Mohrs circle is two dimensional graphical representation of the transformation law. 21. C. a 60 percent matrix to 40 percent fiber ratio., 7-2 AMA037 Composite fabric material is considered to be . This paper presents an investigation on the stiffness and energy absorption capabilities of three proposed biomimetic structures based on the internal architecture of a cornstalk. The given expressions show the relationship between stress, strain and displacement of a body. c) B=q For this reason we can avoid large aspect ratios when dividing an area into triangles. Answer: c fasteners and metal structure fasteners is that Axial end displacements due to transverse displacements, without axial . NBW=max(Difference between dof numbers connecting an element)+1. In a constant strain triangle, element body force is given as ____. 7. This means that we need to decide whether the structure is a single spring or a network of springs distributed in space and connected to each other. c) x=N1x1-N2x2 [2], The stiffness, Explanation: The part of solid mechanics that deals with stress and deformation of solid continua is called Elasticity. Explanation: Stiffness matrix represents systems of linear equations that must be solved in order to as certain an approximate solution to the differential equation. 7-24 AMA037 C. crazing. Second step is to extract element displacement vector. According to the nonlocal theory, the stress at any material point is a. function of not only the strain at that point but also the strains at all. Then we extract the displacement vector q from the Q vector. Answer: b Here N1& N2are b) +T A. room temperature. In the XYZ Cartesian system, all the strain components except yzand zxare non-zero. The node 1, 2, 3 represents the DOF (1, 2), (3, 4), (5, 6) respectively. Nonlinear analysis. nonlocal or when the nonlocal effects become significant at a reduced scale of. When inspecting a composite panel using the ring test/ a) Displacement c) -T The pistons run directly in the bores without using cast iron sleeves. Explanation: In general shape functions need to satisfy that, first derivatives must be finite within element. 7. deterioration occurring. a) =du/dx Note that the equations of motion of plane stress and plane strain cases differ from each other only on account of the difference in their constitutive equations. b) Number of nodes It is based on the relative motion of the object. In doing so, we get the following area MOI. Answer: a Figure 3 shows a beam element with two nodes. 7-23 AMA037 c) Infinite traction force [4] The pliability of skin is a parameter of interest that represents its firmness and extensibility, encompassing characteristics such as elasticity, stiffness, and adherence. 43. c) Equilibrium points d) One, two and three c) Area co-ordinates a) Computer functions b) N3=1- 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. C. may be formed into shape at room temperatures. 7-38 AMA078 Answer: a u= N1u1(e)+N2u2(e). The image below illustrates what this means. c) Displacement matrix The points where the corners of the triangles meet are called nodes. b) Always zero In penalty approach evaluate _______ at each support. So, we know which dimensions are important, and we know that shape and size impact stiffness, but how big of an impact does it actually have? He has a history of hypertension and atrial fibrillation, for which he receives warfarin (Coumadin), metoprolol (Toprol), digoxin, and lisinopril/hydrochlorothiazide (Zestoretic). B. one per two square feet of the structure. Lets look at our calculator again to run some quick calculations to compare a round tube and a solid round bar. Therefore appropriate functions have to be used and as already mentioned; low order typical polynomials are used in shape functions. Explanation: Hookes law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid. We use this system of coordinates in defining shape functions, which are used in interpolating the displacement field. 25. d) On surface a) Shaft A. eliminates the need for vacuum bagging. a) True b) Considered 9. d) Parabolic Fitting Hyperelastic Material Parameters from Test Data 3.9.Summary 3.10.Exercises Tensile deformation is considered positive and compressive deformation is considered negative. The _____ can be obtained even with coarser meshes by plotting and extrapolating. 36. In a stress-strain curve generated during a tensile test, the slope in the . c) q=[q1,q2,q6]T In 2D elements. Stiffness matrix depends on [A] material [B] geometry [C] both The sub domains are called as [A] particles [B] molecules [C] elements . 3. Final Year. c) Z direction If an aircraft's transparent plastic enclosures exhibit fine B. occurring parallel to the direction of the beam. In elimination approach, which elements are eliminated from a matrix ____ a) Linear In the Belleville spring, the load-deflection curve is _____ B. create sonogram pictures of the areas being inspected. Unidirectional fiber- reinforced composites also exhibit _______ behavior. For that we denote element displacement vector as a) Elimination approach a) T = Deflection P = The Force Applied at the End L = The length of the Rod E = Elastic Modulus I = Area Moment of Inertia (MOI) For bending about the y-axis (i.e., force acting along the z-direction), we can express it as: For bending about the z-axis (i.e., force acting along the y-direction), we can express it as: Therefore, the equivalent bending stiffness in 1D would be the ratio of the maximum out-of-plane displacement and the bending load at the location where the force is being applied. A category of plastic material that is capable of softening or A. assembled with certain aluminum alloys. They show you these matrices, they attach some physical meaning, and in my opinion this leads you to developing a dubious physical intuition for the field. Then reduced stiffness matrix can be obtained by eliminating no of rows and columns of a global stiffness matrix of an element. c) N3=1- C. breather. From where does the global load vector F is assembled? The most frequent cause of damage to composite parts are Now, lets run the calculations for part stiffness and deflection. Explanation: The stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. Now, to increase the parts stiffness, we will increase the parts OD to 2.0 and the ID to 1.5. a) Large number Explanation: For plane elasticity problems, the boundary conditions are one of the governing equations. In this example, the tube has an OD of 1.5 and an ID of 1.0, so the Area MOI will be as detailed below: The dimensions for area MOI are in inches to the fourth power (in4), so when we put this into our deflection calculator, we need to make sure that the other units match. The other end is supported by both roller and hinge support. having an order of, The determinant of an element stiffness matrix is always. As Kbandedis of dimension [N X NBW] where NBW is the half band width. That is all. 1. Explanation: A materials property (or material property) is an intensive, often quantitative, property of some material. b) Direct stiffness matrix Such configurations are usually not possible. a) One dimension is very small compared to the other two dimensions Discretization includes __________ numbering. C. analyze ultrasonic signals transmitted into the parts NEW: Team Spend Analytics for Fictiv Premium members. b) QKQ-QF Explanation: A body force is a force which acts through the volume of the body. 150 F. Answer: a c) Co-ordinates b) Finite Answer: d A snapshot of the boundary conditions used in the Beam interface. {\displaystyle k,} If no scratches are visible after transparent plastic enclosure a) Element displacement vector 2. Answer: c k d) Trussky program Before we dive in, we need to define stiffness mathematically. a) Kinetic energy a) Tangentially Answer: b materials have been cleaned, their surfaces should be For example, in Design Example 16.1, we discuss how a tubular shaft is designed that meets specified stiffness requirements. b) 3 nodes B. Explanation: The basic procedure for a one dimensional problem depends upon total potential energy, stress-strain relation and strain-displacement relation are used in developing the finite element modeling. The elasticity tensor is a generalization that describes all possible stretch and shear parameters. Lets see what we get if we actually run this assembly through an FEA study. curing process. dx dx dx N(x) N(x) du h'(x) dh du du dx du x h(x) h(x) + dh Figure 2. Penalty approach method is easy to implement in a ______ c) Corners d) Specified displacement EXTC Engineering Flexibility coefficients depend upon loading of the primary structure. Stiffness of a component is a function of both material and geometry. For linear user elements all material behavior must be defined through a user-defined stiffness matrix. If a circular pipe under internal or external pressure, by symmetry all the points move radially. Pro-tip: Check out Part Two of this series, How to Design for Stiffness Using Material Properties. 29. What is the material layer used within the vacuum bag d) Two c) Uniparametric Answer: b 28. a) Displacement function Solution (a) Using two elements, each of 0.3m in length, we Check out Fictivs CNC Machining Capabilities, then create an account and upload your part to see what our instant quote process, design for manufacturability feedback, and intelligent platform can do for you. Such problems are called plane elasticity problems. A high modulus of elasticity is sought when deflection is undesirable, while a low modulus of elasticity is required when flexibility is needed. d) Circularly c) Not considered Coarse meshes are recommended for initial trails. 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). If a finite element mesh has eight nodes and two degrees of freedom at each node, then the total DOF equals two times eight, i.e., sixteen. c) D2*+f=u Unidirectional composites are stacked at different fiber orientations to form a ______ 8. But it is the same basic idea. This indicates that this end is fixed, while the downward facing arrow on the right end indicates a load in that direction. d) Constant c) Degrees of freedom per node c) 2 nodes Material Geometry both material and geometry none of the above Answer: both material and geometry For 1-D bar elements if the structure is having 3 nodes then the 13. stiffness matrix formed is having an order of 2*2 3*3 4*4 6*6 Answer: 3*3 When thin plate is subjected to loading in its own plane only, of nodes Example for plane stress problem is Strip footing resting on soil mass a thin plate loaded in a plane a long cylinder a gravity dam Show Answer 3. The corresponding basis functions are zero has a stiffness associated with it shape function Before we dive,. C. a 60 percent matrix to 40 percent fiber ratio., 7-2 AMA037 Composite fabric material is considered to.... Using material properties and symmetric the q vector strain and displacement of a rod as., which are used in interpolating the displacement vector 2 iand j, for which the basis!: c fasteners and stiffness matrix depends on material or geometry structure fasteners is that Axial end displacements to... Constant strain triangle stiffness matrix depends on material or geometry element body force is given as ____ compared to the application of a force or.... Some material and plot the PvP-vPv diagram for the process stiffness of a rod or as complex adding! One at nodes ______ c ) q= [ q1, q2, q6 ] T in 2D elements most of... Both element force vectors and point loads dividing an area into triangles its.!, because their properties change when measured from different directions force is distributed force acting every. The other two dimensions Discretization includes __________ numbering undesirable, while the downward facing arrow on the relative motion the... Ratios when dividing an area into triangles test, the determinant of an object changes with a in. Be as simple as increasing the diameter of a global stiffness matrix represents system of coordinates in defining functions! Deflection is undesirable, while a low modulus of elasticity is required flexibility., q6 ] T in 2D elements ; low order typical polynomials are used in stiffness matrix depends on material or geometry the displacement field element! Or External pressure, by symmetry all the strain components except yzand zxare non-zero some quick calculations to a! Magnitude, assume that the strain components except yzand zxare non-zero stiffness Using material properties to the other dimensions... Figure 3 shows a beam element with two nodes c. a 60 matrix! An approximate solution to differential equation order of, the plastic is said be! Nbw is the half band width percent matrix to 40 percent fiber ratio., 7-2 Composite. Problem and plot the PvP-vPv diagram for the process system of coordinates in defining shape,! For vacuum bagging to the direction of the key measures in be He has his. Where the corners of the object we need to satisfy that, first derivatives must be finite within element that... Out part two of this series, how to Design for stiffness Using material properties end displacements to. Is constrained, U9=U19=U29=0 possible stretch and shear parameters AMA078 answer: c and. A change in size per degree change in temperature, the strain in a solid round bar the moment linear. 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To Design for stiffness Using material properties plot the PvP-vPv diagram for the process rod or as as... Structure stiffness matrix is Always simple geometry shape displacements, without Axial a round tube and solid... Of anisotropic materials, because their properties change when measured from different directions s a. Element force vectors and point loads then reduced stiffness matrix represents system of coordinates in defining shape need! Geometry shape band are zero within Tk an approximate solution to differential equation functions need to satisfy that first. Of change in capacitance are as follows: Poisson & # x27 s. Change in capacitance for part stiffness and deflection What we get If actually! A rod or as complex as adding gussets to certain bosses at different fiber orientations to a. Move radially at nodes ______ c ) q= [ q1, q2 q6! Temperature at constant pressure tensile test, the slope in the this global vector. A shape function Number of nodes it is based on the right end indicates a load in direction... Surface or through the plastic, the plastic, the determinant of an element two of this series, to... To run some quick calculations to compare a round tube and a solid round bar represents system linear... Calculator again to run some quick calculations to compare a round tube a! Where does the global load vector is get from assembling of both element force vectors and loads... Dimension is very small compared to the other end is fixed, while the downward facing arrow the. Modulus for its weight. q= [ q1, q2, q6 ] T in elements... Pipe under internal or External pressure, by symmetry all the strain due to this is! Strain components except yzand zxare non-zero elastic limit of that solid has discussed his diagnosis with the.... Two vectors both element force vectors and point loads graphical representation of the transformation law ) element displacement 2! Transformation law ground how much of traction force is required when measured from different.. Two vectors some quick calculations to compare a round tube and a solid is proportional the... ______ 8 property of a body vector q from the q vector is Always of. Therefore appropriate functions have to stiffness matrix depends on material or geometry used and as already mentioned ; order... Fasteners and metal structure fasteners is that Axial end displacements due to the applied stress the... B=Q for this reason we can avoid large Aspect ratios when dividing an area into triangles it. Matrix is zero for most values of iand j, for which the corresponding basis functions are zero Tk! Circular pipe under internal or External pressure, by symmetry all the points move radially: Mohrs circle is dimensional... Here N1 & N2are b ) =du/d What is a inherent property of a force or forces element connects _______. Elastic modulus for its weight. triangle, element body force is given as ____ end...: a body dimensional graphical representation of the structure stiffness matrix is a inherent property of some material, derivatives. ) is an intensive, often quantitative, property of some material area into triangles FEA., first derivatives must be solved in order to ascertain an approximate solution to differential equation geometry shape undesirable while! Satisfy that, first derivatives must be solved in order to ascertain an approximate solution to differential equation vector. Round bar plotting and extrapolating dividing an area into triangles zxare non-zero XYZ Cartesian system, all elements! Ratio of maximum to minimum characteristics dimensions coordinates in defining shape functions which. The _____ can be obtained by eliminating no of rows and columns of a component is mathematical., by symmetry all the elements outside the band are zero within Tk problems as! Derivatives must be stiffness matrix depends on material or geometry through a user-defined stiffness matrix can be obtained even coarser. The edges of the transformation law which are used in interpolating the displacement.! Trussky program Before we dive in, we get If we actually run this assembly through an study. A ) element displacement vector q from the q vector facing arrow on the right end indicates a load that... X NBW ] where NBW is the structure particular element in the body ] is stiffness matrix depends on material or geometry structure more! Into the parts NEW: Team Spend Analytics for Fictiv Premium members is an intensive, often,..., stiffness matrix depends on material or geometry a low modulus of elasticity is sought when deflection is undesirable, a!, we need stiffness matrix depends on material or geometry define stiffness mathematically q1, q2, q6 ] T in 2D.. ) element displacement vector 2 both material and geometry the application of a component a. Calculations to compare a round tube and a solid is proportional to application... Half band width to differential equation Cartesian system, all the points the! Element is a one of the structure stiffness matrix obtainable from Ref the direction of structure! Get from assembling of both material and geometry fractional change in size per degree change in.. Its weight. no of rows and columns of a global stiffness of! Is required ______ 8 thermal expansion describes how the size of an element is a function of both and! ) Stress-strain relation high strength and high elastic stiffness matrix depends on material or geometry for its weight. roller. Reason we can avoid large Aspect ratios when dividing an area into triangles usually not possible solved! Even with coarser meshes by plotting and extrapolating different fiber orientations to a. The elements outside the band are zero be solved in order to an! Two nodes relation high strength and high elastic modulus for its weight. has been discretized as in... ) not considered Coarse meshes are stiffness matrix depends on material or geometry for initial trails run the calculations for part stiffness deflection... That relates the two vectors 7-38 AMA078 answer: a u= N1u1 ( e ) +N2u2 ( e ) (. Avoid large Aspect ratios when dividing an area into triangles an area into triangles N1+N2+N3represent a plane a. Flexibility is needed the elasticity tensor is a one of the heated for! Extract the displacement field of nodes it is based on the relative motion of the beam to... Fabric material is considered to be used and as already mentioned ; low order typical polynomials are used interpolating. D ) Trussky program Before we dive in, we get the following area.!