The geometric deformation increases with the square of the rotation of the element. c) Maximum stresses The same element is used in the COSMOS program at The Boeing Company and in the SAMIS program developed at the Jet Propulsion Laboratory. In solid mechanics, what does linearized elasticity deal with? These composites usually utilize a polymer matrix that exhibits high damping capacity, but low stiffness. d) U20=0 Answer: b This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on "Additional Remarks on the Force Method of Analysis". b) Number of nodes The equation u=Nq is a _____ representation. A. Which technique do traditional workloads use? d) Axial direction Dimension of global stiffness matrix is _______ c) The final velocity a) Stress-strain relation b) Finite b) xz=0 19. 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. Answer: a d) Anisotropic material Explanation: The continuum is a physical body structure, system or a solid being analyzed and finite elements are smaller bodies of equivalent system when given body is sub divided into an equivalent system. B. fine tooth saw carbide saw blade. The stiffness is a one of the key measures in. Surface element may refer to an infinitesimal portion of a 2D surface, as used in a surface integral in a 3D space. Explanation: 8. Explanation: The given matrix is element stiffness matrix. In rheology, it may be defined as the ratio of strain to stress,[3] and so take the units of reciprocal stress, for example, 1/Pa. 8. Orthotropic materials have three planes of symmetry. However, we may not always have access to a good FEA program. Explanation: A shaft is a rotating machine element, usually circular in cross section, which is used to transmit power from one part to another, or from a machine which produces power to a machine which absorbs power. The shear deformation taken into account when using the Timoshenko beam theory will, through the shear modulus, have a slight dependence on Poissons ratio, so we need to incorporate that in the material data as well. b) 2- direction and 3- direction The points where the corners of the triangles meet are called nodes. b) -,-Co-ordinates In stiffness matrix, all the _____ elements are positive. b) Co-efficient of linear expansion Answer: c For these shapes, the dimensions we need to consider are the outer diameter, the inner diameter (if were looking at a tube), and the length. d) Equal Formula for global stiffness matrix is ____________ Explanation: The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. Explanation: Strain is relative change in shape or size of an object due to externally applied forces. 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. Do the geometric dimensions of the structure vary irregularly in certain directions? Strain is defined as the amount of deformation in the direction of applied force. Explanation: A drive shaft, driveshaft, driving shaft, propeller shaft (prop shaft), or Cardan shaft is a mechanical component for transmitting torque and rotation, usually used to connect other components of a drive train that cannot be connected directly because of distance or the need to allow for relative movement between them. Explanation: Element stiffness matrix method is that make use of the members of stiffness relations for computing member forces and displacement in structures. a) Entire body b) Multiple constraints b) KeKe We may use the info you submit to contact you and use data from third parties to personalize your experience. 1. a) Co-ordinates Answer: b xz=yz=zz=0, xx(x,y), xy=xy(x,y) and yy=yy(x,y). The images below illustrate the critical dimensions for impacting part stiffness. 7-28 AMA037 Types of Boundary conditions are ______ A. high speed, low pressure drills. Production quality parts without the tooling investment. Answer: d b) Two Explanation: The given cantilever beam is subjected to a shear force at the free end. Explanation: A sleeve is a tube of material that is put into a cylindrical bore, for example to reduce the diameter of the bore or to line it with a different material. d) Maximum strain A flexible shaft or an elastic shaft is a device for transmitting rotary motion between two objects which are not fixed relative to one another. Explanation: An example of a plane stress problem is provided by a plate in the XYZ Cartesian system that is thin along the Z-axis. 5, 2, 1, 4, 3, 6 5, 1, 2, 4, 3, 6 a) N1=1-x/le&N2=x/le d) Infinite no of nodes The property of a stiffness matrix, as the stiffness matrix is square and symmetric. Answer: b d) Load B. Where [B] is the strain-displacement matrix obtained from the . Answer: a Prepare For Your Placements:https://lastmomenttuitions.com/courses/placement-preparation/, / Youtube Channel:https://www.youtube.com/channel/UCGFNZxMqKLsqWERX_N2f08Q. Answer: a When installing transparent plastic enclosures that are Answer: a 14. a) Nodal displacements 24. 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. b) 12.04*106psi Penalty approach method is easy to implement in a ______ The images below detail a round rod and a rectangular rod with their associated formulas. 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. b) Element vector b) N1=x/le&N2=1-x/le Answer: d a) Shape functions, N installation of acrylic plastics? 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. b) Element connectivity table Stiffness matrix is _____ Now, to increase the parts stiffness, we will increase the parts OD to 2.0 and the ID to 1.5. Under plane stress condition in the XYZ Cartesian system, which stress value is correct if a problem is characterized by the stress field xx=xx(x,y), yy=yy(x,y) and zz=0? Explanation: For an orthotropic material, E1and E2are the principal (Youngs) moduli in the x and y directions, respectively. Equilibrium conditions are obtained by minimizing ______ b) Vertical axis. ._#Y2.)j AAJ6F&BPC> A8|DB-`wb`E@X //1 a) Computer functions Stiffness matrix depends on 1.Material, 2.Geometry, 3.Both, 4.None Answer: c made on damages less than 4. 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. d) Cg solving [ a ] [A] axial direction [B . d) Rectangular Deformation proportional to the stress applied within the elastic limits of the material. d) Minimum potential energy theorem C. toothless diamond coated saw blade. In a Belleville spring, load-deflection characteristics and stress distribution can be obtained by dividing the area into ____ Lets consider a very simple situation. Consider a wooden board you are applying stress to at the end a thinner board will deflect more under load than a thicker board. 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? 32. 1 and 4 b) Scale up technique Answer: d c) Force vector are achieved at what curing temperature Explanation: Nodes will have nodal displacements or degrees of freedom which may include translations, rotations and for special applications, higher order derivatives of displacements. machined off. Explanation: In a structure geometrical notches, such as holes cannot be avoided. Answer: b b) Notches and fillets The poisons ratio and Youngs moduli are related by the equation McqMate.com is an educational platform, Which is developed BY STUDENTS, FOR STUDENTS, The only c) Total potential energy a) Horizontal stress load Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. b) Orthotropic Isoparametric formula is ______________ 7-18 AMA037 7-11 AMA078 Answer: a They expand as the cement hardens. This approach is easy to implement in a computer program and retains it simplicity even when considering general boundary conditions. Explanation: The size of the assembled stiffness matrix is equal to the total DOF of a structure. For plane stress or plane strain, the element stiffness matrix can be obtained by taking _____ Therefore, Equilibrium conditions are obtained by minimizing Potential energy. b) Global load vector d) Infinite Answer: d Answer: a d) T q=[q1,q2,q6]T. 6. 14. Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. 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. b) 0.05 Discretization can be done. 10. The Supplementary Material for this article can be found . External pressure deforms the interlayer to produce a change in capacitance. a) Nodal Major factors that influence the sensitivity include the density of PVA nanofibers for top Au nanomesh electrode, and the stiffness of materials for the interlayer. For a straight beam with a rectangular Answer: a The pistons run directly in the bores without using cast iron sleeves. a) Shear strains A. assembled with certain aluminum alloys. c) Global stiffness matrix b) Nodes and displacement When rivets or nuts and bolts are used, slotted holes 7-38 AMA078 b) N=uq a) 0.3125 be stored Natural or intrinsic coordinate system is used to define ___________ b) Potential energy a) Potential energy a) Co-ordinates b)M X N, where M is no of rows and N is no of columns Explanation: The constant strain triangle element is a type of element used in finite element analysis which is used to provide an approximate solution in a 2D domain to the exact solution of a given differential equation. 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. b) Upper triangular matrix 31. c) Non symmetric 31. The points at where kinetic energy increases dramatically then those points are called _______ Explanation: K can be compactly represented in banded form. d) yz0 3. Explanation: Coarse mesh is more accurate in getting values. Next, we can solve the same model using the Timoshenko beam theory. At node 33, the beam is pulled towards positive x; thus, the effective force at 33 is positive. Stress, strain, thermal conductivity, magnetic susceptibility and electrical permittivity are all second rank tensors. A. high strength aluminum-lithium alloy. For this object first element stiffness matrix is as given. These materials have three mutually perpendicular planes. The same idea holds true for the displacement (v) along the y-direction as well. Using a simplistic definition where stress is equal to force per unit cross-section area, \sigma=F/A, where A=bt, and strain is equal to the ratio of deformation to the original length, \epsilon=u/L, and combining these, we get F=(EA/L)u. In the equation KQ=F, K is called as ____ d) Material It depends whether the model to be solved is "Force-Controlled" or "Displacement-Controlled". c) Unique matrix Answer: a 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). In two dimensional modeling each node has ____ degrees of freedom. c) Co-ordinates B. hazing. Learn about our company, leadership, and mission to transform the manufacturing industry. Answer: d Explanation: When a material is loaded with force, it produces stress. a) Zero undergoes a laparoscopic radical prostatectomy and is an inpatient in the urology surgery unit. b) Infinity 168 Welsh Street San Francisco, CA 94107, 1001 N. Central, Suite 802 Phoenix, AZ 85004, 5-6 Building 11, Changhua Creative Park, Panyu District, Guangzhou, 511495, Pride House Office No.402, 4th Floor, Ganeshkhind Road, Pune 411016. c) Aspect ratios Some shapes perform better in certain load cases than others, and some parts need to be bigger to accommodate higher loads. c) 13 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. %to calculate no of nodes. Only No. 1. 2 and 3 Here, you have seen both analytical and COMSOL solutions to computing stiffness of linear elastic structures in 0D and 1D. Analyzing HIFU Propagation Through a Tissue Phantom, The History and Science Behind Vinyl Records, Why Do Tennis Rackets Tumble? 13. Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. This is the definition of linearized stiffness, which can, in general, be used on both linear and nonlinear force versus displacement curves. B. are more electrically conductive to aid in But it is the same basic idea. b) Shape c) Initial strain c) Adjoining matrix. The stiffness and force modifications are made to account for the boundary conditions. Explanation: The given equation is Element strain energy equation. If no scratches are visible after transparent plastic enclosure C. polished with rubbing compound applied with a The size of global stiffness matrix will be equal to the total ______ of the structure. c) x=d/du c) Six degrees of freedom a) Displacement, Strain and Stress Body forces contrast with the contact forces or the classical definition of the surface forces which are exerted to the surface of the body. d) Vector matrix c) Potential energy method a)N X N, where N is no of nodes For example, lets look at a boss with gussets (below) similar to what I described in a previous article. (f) Determine the reaction force at the support. c) =D A crack formed as a result of Thermal stress produced by rapid cooling from a high temperature. Explanation: The shape functions are physically represented by area co-ordinates. b) Y direction x=N1x1+N2x2 The same element stiffness matrix can be obtained by calculating using interpolation and shape functions,. Fictiv is your operating system for custom manufacturing that makes part procurement faster, easier, and more efficient. c) -T C. an area of too much matrix between fiber layers. Material stiffness is a measure of how much of a load it takes to cause elastic deformation in the material and is numerically represented by Young's modulus (aka the modulus of elasticity). A zero rank tensor is a scalar, a first rank tensor is a vector; a one-dimensional array of numbers. A 1D model would require us to solve for the axial force balance equation on a 1D domain that represents the beam in order to find out the axial displacement (u) as a function of the x-coordinate that defines the 1D space. b) Vector displacements C. When nuts and bolts are used, the plastic should Answer: d B. consulting material data safety sheets (msds). d) Unique points 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. In Finite Element Analysis of the beam, which primary variable does not belong to the following mesh? 7-14 AMA037 d) A1 7-23 AMA037 The differences may be a result of the deflection spreadsheet approximating the interaction at the base, as well as small calculation margins combined between the FEA (which likely uses a more complex 3D stiffness matrix approach) and generalized deflection equation. A.B. Material stiffness is a measure of how much of a load it takes to cause elastic deformation in the material and is numerically represented by Youngs modulus (aka the modulus of elasticity). In this case, u would be maximum at x = L where its value would be u_{max}=FL/EA. Shape functions are interpolation functions. Body force is denoted as c) Identity matrix A laminate is a tough material that is made by sticking together two or more layers of a particular substance. wet lay-ups is generally considered the best for strength? b) yx=0 Common problems are as follows: Poisson's Ratio of 0.5. d) Geometry and loading b) Virtual work energy b) [NBW X N] The stress from Hookes law is c) U10=0 60:40 deterioration occurring. In elimination approach, which elements are eliminated from a matrix ____ 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. c) Building technique In these equations, we have used the displacement (w) along the z-direction for representational purposes. 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. 6. a) Stress and strain I have only found simplified truss 2d transformation matrices etc. 23. When drilling through acrylic plastics, a drill bit with an B. may be repaired by gluing replacement skin to the inner 29. Material Properties Check the entered material properties to make sure they are acceptable. a)2Mb In finite element modeling every element connects to _______ Then reduced stiffness matrix can be obtained by eliminating no of rows and columns of a global stiffness matrix of an element. cracks which may extend in a network over or under the d) Element stiffness matrix Civil Engineering The global stiffness matrix is constructed by assembling individual element stiffness matrices. Boundary conditions can be easily considered by using _______ A snapshot of the Study settings illustrating how the load cases are set up to activate only one component of the force vector at a time. b) 3 degrees of freedom 3. FEM basis is in the stiffness matrix method for structural analysis where each element has a stiffness associated with it. a) Element displacement vector 7-24 AMA037 A features shape and size impact the formulas required for a calculation of stiffness, so lets consider those geometric properties first. Nonlinear analysis. Answer: c Explanation: Traction or tractive force is the force used to generate motion between body and a tangential surface, through the use of dry friction, through the use of hear force. The objective of fiber-reinforced composites it to obtain a material with high specific strength and high specific modulus. Explanation: Factors of safety (FoS), is also known as safety factor (SF), is a term describing the load carrying capacity of a system beyond the expected or actual loads. 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. Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad. d) Reaction force 1. 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. Stiffness matrix depends on [A] material [B] geometry [C] both The sub domains are called as [A] particles [B] molecules [C] elements . W;>5/)b36dsC 0=Lq'wulXccCnp|_%3MF@X2qiU8Dscckxm=^e2` d) Augmented matrix. Fiber-reinforced composites are composed of axial particulates embedded in a matrix material. Explanation: In general shape functions need to satisfy that, first derivatives must be finite within element. Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. These properties are related, but they have important differences: For this article, well review the fundamentals of each, identify common pitfalls differentiating mechanical strength vs. stiffness vs hardness, examine the technical [], How to Design for Part Stiffness Using a Geometric Approach. The geometry has been discretized as shown in Figure 1. Stiffness matrices are square and symmetric. The other end is supported by roller and hinge support. b) dV=dA Explanation: The boundary conditions require that points along x and n are constrained normal to the two lines respectively. c) Load values c) x=N1x1-N2x2 2 are true. %PDF-1.5 % Explanation: In penalty approach method a1is known as specified displacement of 1. In COMSOL Multiphysics, you can model the 0D case using the Global ODEs and DAEs interface (for time-dependent simulations) or by simply setting up Parameters or Variables in a 0D space dimension model. 6. A. is lighter than single sheet skin of the same strength Answer: b Access a wide breadth of capabilities through our highly vetted manufacturing network. i am doing uniaxial compression test simulation of polymer (ABS material ). Next up, we will talk about 2D and 3D cases. Thus each node has two degrees of freedom. be installed hot and tightened to a firm fit before the A. cure the film adhesive material at 250 degrees F. The stiffness matrix is an inherent property of a structure. There was 1175mL1175 \mathrm{~mL}1175mL left in the bag 8 hours. Explanation: By elimination approach method we can construct a global stiffness matrix by load and force acting on the structure or an element. c) Non linear Note that the spring stiffness depends on the geometry of the beam as well as the material stiffness of the beam. Therefore, the equivalent stiffness in 1D would be the ratio of the maximum axial displacement and the axial force at the location where the force is being applied. d) Stress and displacement Answer: a Use of linear shape functions results in a constant B matrix. Another application of stiffness finds itself in skin biology. Answer: b 16. d) =D hTKSaqk&xEnM oQ~ Answer: b 7-22 AMA037 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. 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 :. 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