stiffness matrix depends on material or geometry

Answer: d When an orthotropic plate is loaded parallel to its material axes, it results normal strains. A node is a co-ordinate location in space where degrees of freedom are defined. c) Principal axes Here is the workflow for obtaining the stiffness from the 1D model: A snapshot of the 1D model made using the Beam interface. (c) Assemble the structural stiffness matrix Kand global load vector F. (d) Solve for the global displacement vector d. (e) Evaluate the stresses in each element. a) Global displacement vector A. high speed, low pressure drills. The approach shown here for evaluating the stiffness components is applicable as long as we do not expect any coupling between extension and bending, (i.e., when the stiffness matrix is diagonal). C. any of the metals commonly used in aircraft fasteners. In order to incorporate this effect, we would need to create at least a 1D model. 90 degrees a) Radially By element stiffness matrix we can get relation of members in an object in _____ For that we denote element displacement vector as In general shape functions need to satisfy that, displacements must be continuous across the element boundary. d) Co-ordinates The gussets are added to increase the part stiffness and strength, but how do we calculate this without extensive hand calculations? a) Load vector a) True 7. 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. Only T2T_2T2 is given; how do you determine the second property of the final state? d) Radius 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) Structure b) Normal strains "#HHH N Answer: d %PDF-1.5 % 8. Answer: b At least for a physical spring. Interpolation within the shape functions is achieved through shape functions. Answer: a of elements Explanation: Nodes will have nodal displacements or degrees of freedom which may include translations, rotations and for special applications, higher order derivatives of displacements. B. This further reduces the number of material constants to 21. Explanation: A materials property (or material property) is an intensive, often quantitative, property of some material. PDFs for offline use. We take free online Practice/Mock test for exam preparation. Each MCQ is open for further discussion on discussion page. All the services offered by McqMate are free. d) Load Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. 7-30 AMA037 retained by bolts extending through the plastic material and The Dzhanibekov Effect Explained. 29. How many nodes are there in a hexahedron element? a)N X N, where N is no of nodes d) Load There are two types of boundary conditions, namely, essential boundary conditions and natural boundary conditions. Answer: a b) Nodes However, it also translates to the idea that each of these springs has its own stiffness. Finite element method uses the concept of shape functions in systematically developing the interpolations. The points where the corners of the triangles meet are called nodes. Hence, the deformation or displacement (u) is not the same at each cross section along the length. Lets see what we get if we actually run this assembly through an FEA study. Explanation: The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. a) Force d) Nodes Explanation: The isoparametric representation of finite elements is defined as element geometry and displacements are represented by same set of shape functions. Boundary conditions can be easily considered by using _______ The global stiffness matrix is constructed by assembling individual element stiffness matrices. A. in a vacuum sealed environment. to transition to a different internal structure. Hence, in a constant strain within the element. 28. Answer: b a) D*+f=u Answer: c b) Considered In a stress-strain curve generated during a tensile test, the slope in the . c) Polynomial a) High traction force Answer: d d) Undefined d) Stress displacements of nodes*Degrees of freedom per node. But 50% of consumer electronics products fail EMC testing during their first pass. 3. As I mentioned previously, all shapes will have a different formula for area MOI. 1. applying external heat. One dimensional element is the linear segments which are used to model ________ Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. They produce a hazy residue and should be used only b) Low traction force d) On element 16. N1, N2, N3 are not linearly independent only one of two of these are independent. d) Unidirection composite In particular, N1+N2+N3represent a plane at a height of one at nodes ______ c) yz0 It is denoted by symbol . b) Degrees of freedom A simulation geometry is made by digital microscope measurements of the specimens, and a simulation is conducted using material data based . Answer: a 11. a) A1/A In general, when there are non-linear effects, either due to material, geometry or boundary condition non-linearity (contacts), then the element or structural stiffness matrix tends to get non-symmetric during the analysis. Others.. core material with thermoplastic resin. 18. Answer: b b) Deformation If no scratches are visible after transparent plastic enclosure A. no fewer than three. b) T=[Tx,Ty]T A.B. 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. In the penalty approach, rigid support is considered as a spring having stiffness. Explanation: The constant strain triangle or cst 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. m d) Infinite no of nodes self-locking nuts, the nuts should be tightened to a 39. 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. 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. Note that the spring stiffness depends on the geometry of the beam as well as the material stiffness of the beam. A Belleville washer is a type of spring shaped like a washer. In particular, for basis functions that are only supported locally, the stiffness matrix is sparse. A. He has discussed his diagnosis with the urologist. A. assembled with certain aluminum alloys. c) Real number Answer: a Explanation: Strain is defined as a geometrical measure of deformation representing the relative displacement between particles in a material body. Here, we can see that we got about 0.163 of deflection at the end. Answer: a d) Either nodal or elemental This method is used to derive boundary conditions. composite construction is c) Total potential energy This is exactly what wed expect, based on the linear relationship Area MOI has on the output of the deflection and stiffness equations. Two Dimensional Finite Element Formulation, https://lastmomenttuitions.com/courses/placement-preparation/, https://www.youtube.com/channel/UCGFNZxMqKLsqWERX_N2f08Q. Explanation: When the workload increases on the system, the machine scales up by adding more RAM, CPU and storage spaces. a) Co-ordinates 5. Coarse mesh is more accurate in getting values. c) N3=1- Due to the thicker boards increased cross-sectional area (geometry), it can handle a greater applied load before deflecting. c) q=[q1,q2,q6]T 9. 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. c) -T A rigid body is usually considered as a continuous distribution of mass. a) Loading a) Shaft The pistons run directly in the bores without using cast iron sleeves. 7-21 AMA037 One source of truth for team spend by project. Answer: d d) Total potential energy; Stress-strain relation; Strain-displacement relation. b) x=N2x1+N1x2 Only No. Answer: c The stiffness is a one of the key measures in. That is all. Specifically, it measures the fractional change in size per degree change in temperature at constant pressure. The most general anisotropic linear elastic material therefore has 21 material constants. B. d) Load vector 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: An element is a basic building block of finite element analysis. In biology, the stiffness of the extracellular matrix is important for guiding the migration of cells in a phenomenon called durotaxis. Thus, xx, xyand yyare non-zero stresses. a) Large number b) KeKe [k] is the structure stiffness matrix that relates the two vectors. Stresses due to rigid body motion are _______________ The unknown displacement field was interpolated by linear shape functions within each element. Explanation: Orthotropic materials are a subset of anisotropic; their properties depend upon the direction in which they are measured. Stiffness Matrix to solve internal forces in 1D (Part 1 of 2) - Finite Element Methods Blake Tabian 34K views 6 years ago Derivation of stiffness matrix of 1D element Nivrutti Patil 7.3K. Answer: c What is meant by stiffness matrix? a) Topaz For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. In solid mechanics, what does linearized elasticity deal with? a) Identity matrix T=[Tx,Ty]T. 10. b) Degrees of freedom a) Entire body c) Geometry and strain FEM basis is in the stiffness matrix method for structural analysis where each element has a stiffness associated with it. At node 33, the beam is pulled towards positive x; thus, the effective force at 33 is positive. A global stiffness matrix K is a banded matrix. a) Nodes and elements b) Element In penalty approach evaluate _______ at each support. a) The initial displacement and velocity Stiffness matrix is _____ Hi Sreenivas, Geometric Stiffness Matrix is often used in Buckling. While considering longitudinal stresses and vertical stresses in a horizontal beam during bending. b) False Understanding the definition of stiffness Knowledge of the mechanical properties of materials. Answer: c Element stiffness is obtained with respect to its ___ The size of global stiffness matrix will be equal to the total ______ of the structure. c) Elements Therefore by this relation element stiffness matrix can be obtained by material property matrix. c) Displacement vector In q=[q1,q2]Tis defined as __________ d) 7.50*106psi c) Vector displacements C. consulting AC43.13 section 1B. d) Trussky program For an orthotropic material, if E and v represent Youngs modulus and the poisons ratio, respectively, then what is the value of v12if E1=200 Gpa, E2=160 Gpa and v21=0.25? b) Quadratical d) Two In the International System of Units, stiffness is typically measured in newtons per meter ( (f) Determine the reaction force at the support. Traction force is a distributed load along the surface of a body. a) Force and load Read Part 2 to learn how to compute the stiffness of linear elastic structures in 2D and 3D. b) xz=0 Explanation: =Bq Answer: a B. c) A Global Evaluation is used to print the values of kxx, kyy, and kzz. W;>5/)b36dsC 0=Lq'wulXccCnp|_%3MF@X2qiU8Dscckxm=^e2` Both Solidworks and CREO/ProE have this function, which is especially useful when looking at complex geometries. c) uT c) Computer program d) yy=0 That is, the modulus is an intensive property of the material; stiffness, on the other hand, is an extensive property of the solid body that is dependent on the material and its shape and boundary conditions. Explanation: Element stiffness matrix method is that make use of the members of stiffness relations for computing member forces and displacement in structures. d) Uniform stiffness matrix 25. v12indicates that the poissons ratio that characterizes the decrease in ______ during tension applied in ______ d) Assembling ). 4. Material Properties Check the entered material properties to make sure they are acceptable. The load at which buckling occurs depends on the stiffness of a component, not upon the strength of its materials. Explanation: Strain is relative change in shape or size of an object due to externally applied forces. degrees of freedom a The elasticity matrix as far as I know defines the effective Youngs Modulus in various directions for an an-isotropic crystal so essentially yes but only for anisotropic materials. The shape functions are precisely represented as 4. In industry, the term influence coefficient is sometimes used to refer to the coupling stiffness. 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. c) U10=0 2. Answer: d Explanation: The given matrix is element stiffness matrix. We know that Stiffness matrix depends on [A] material [B] geometry [C] both The sub domains are called as [A] particles [B] molecules [C] elements . Answer: d Explanation: The shape function is function which interpolates the solution between discrete values obtained at the mesh nodes. The stiffness matrix is an inherent property of the structure. A. water from between the laminations. 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. d) Unique points a) Degrees of freedom The COMSOL software also allows you to use the Timoshenko beam theory, which would be more appropriate for the accurate 1D modeling of low aspect ratio structures. be stored d) Thermal effect geometry/distribution, and properties of the con-stituent phases, it is possible to design materials with property combinations that are better than those found in the metal alloys, ceramics, and polymeric materials. Explanation: The total potential energy of an elastic body is defined as sum of total strain energy and the work potential energy. This article is part one of a two-part series that discusses different methods for increasing part stiffness. Explanation: The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. 28. B. consulting material data safety sheets (msds). This gives us a linear force versus displacement relationship, such that the stiffness is independent of the operating point as well as any spatial variation in force, displacement, and material properties. 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. a) T B. d) N1=x & N2=0 Explanation: Galerkin method provides powerful numerical solution to differential equations and modal analysis. d) Sleeve and couple a)2Mb c) Y direction The expressions u=Nq; =Bq;=EBqrelate ____________ Explanation: Stiffness matrix represents systems of linear equations that must be solved in order to as certain an approximate solution to the differential equation. 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. b) Nodes Use of quadratic interpolation leads to more accurate results. 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. Dry fiber shop procedures less messy than In this case, a 0D model is also a single degree of freedom (SDOF) representation of the beam. In engineering approach to FEM in Structural Mechanics, how it is presented, you lose the feeling that you are solving Partial Differential Equations. c) Singular stiffness matrix FDM, SLS, SLA, PolyJet, MJF technologies. d) =D Answer: b Low order polynomials are typically chosen as shape functions. For linear user elements all material behavior must be defined through a user-defined stiffness matrix. Answer: 2 Stiffness matrix depends on 12. c) Lower triangular matrix When installing transparent plastic enclosures that are C. 250 - 300 F. c) Non linear Explanation: Coarse mesh is more accurate in getting values. Wood may also consider to be orthotropic. By signing up, you agree to our Terms of Use and Privacy Policy. c) Iterative function 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. B. dissolves in organic solvents. He was told about his Gleason score but is not sure what this is. c) Degrees of freedom per node Answer: a Displacement is the difference between the final and initial position of a point. Write the element stiffness for a truss element. a) Elastic energy As Kbandedis of dimension [N X NBW] where NBW is the half band width. Answer: a These effects result in a stiffness matrix which is . We will explore these cases here. c) Linear a) 2- direction and 1- direction Answer: d Answer: a Copyright 2021 Quizack . b) Material property matrix, D k For this reason we can avoid large aspect ratios when dividing an area into triangles. Now, lets run the calculations for part stiffness and deflection. An element is a mathematical relation that defines how the degrees of freedom of a node relate to next. structures, a change in sound may be due to damage or damp cloth. (9) leads to the stiffness matrix Ko of a stable ele-ment in C. Thus, the remaining tenn in Eq. Explanation: The given cantilever beam is subjected to a shear force at the free end. 7. b) =D Answer: a It is important to note that the stiffness matrix is symmetric only in this simple case of linear elastic and static problems. Thank you for your comment and interest in this blog post! dx dx dx N(x) N(x) du h'(x) dh du du dx du x h(x) h(x) + dh Figure 2. Stiffness matrix represents a system of ________ 24. This is especially true if you dont use them on a regular basis, so Ill go over the process to clarify the math. b)M X N, where M is no of rows and N is no of columns This is why plastic coat hangers have a larger diameter (cross-sectional area) than metal hangers. Explanation: A degrees of freedom may be defined as, the number of parameters of system that may vary independently. How can I put the real number of stiffness constant to a membrane? Modeling of a cylinder of infinite length subjected to external pressure. In shape functions, _________ must be continuous across the element boundary. a) Body force 4. Body forces contrast with contact forces or the classical definition of surface forces which are exerted to the surface of the object. All of the commands start with a * character and look and act like standard APDL commands. 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. 6. Explanation: The part of solid mechanics that deals with stress and deformation of solid continua is called Elasticity. 11. We will compute the stiffness of this beam both analytically and using COMSOL Multiphysics, comparing the solutions obtained from these two methods. a) Displacement function Explanation: The size of the assembled stiffness matrix is equal to the total DOF of a structure. 7-24 AMA037 function [stiffness_matrix] = global_stiffnesss_matrix (node_xy,elements,E,A) - to calculate the global stiffness matrix. b) QKQ-QF 7-36 AMA037 a) Thermal expansion N [1], The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Which is the correct option for the following equation? 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. A. removes excess resin uniformly from the structure. Look at earlier problem and plot the PvP-vPv diagram for the process. d) Matrix b) dV=dA c) No degrees of freedom d) Small deformations in non-Hookean solids 7-17 AMA037 c) Non symmetric Explanation: Penalty approach is one of the method to derive boundary conditions of an element or a structure. 27. 17. d) Linear 2 are true. A 1D representation of the beam, obtained using the balance of static axial forces in the body. C. impacts to the surface by debris. be installed hot and tightened to a firm fit before the a) Displacement M d) 2 c) Transverse axis. a) Stiffness matrix a) Tangentially In stiffness matrix, all the _____ elements are positive. Potential energy =1/2[QTKQ-QTF]. 20. For a straight beam with a rectangular are best avoided by d) T Materials have a long shelf life. d) Anisotropic material undergoes a laparoscopic radical prostatectomy and is an inpatient in the urology surgery unit. 60:40 b) Element connectivity table 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. 7-13 AMA037 What is the Global stiffness method called? Orthotropic planes have ____ mutually perpendicular planes of elastic symmetry. Read the latest news about Fictiv and access our Press Kit. 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. Principal stresses and their directions are calculated by using ____ dV=tdA. 15. (coin tap) test. d) 44 a) xx=0 Continuum is discretized into_______ elements. d) Thermal stress Answer: b Also worth noting is the stiffness performance of the tube as compared to solid bar stock. b) uTT i want stress v/s strain graph of the above . det(Ko + K.) = 0 (20) Geumetric Sti ffncss ]\'Iatrix The del"ivation ofstiffness matrices for finite elements often is based on 1111 approximate displllccment field of . Explanation: Elasticity is the part of solid mechanics that deals with stress and deformation of solid continua. d) On surface b) Force Hence, we can express the axial stiffness of the beam for this 0D model with the following equation: Assuming the Youngs modulus of steel is 200 GPa, we find that the axial stiffness of the beam is k = 4109 N/m. 24. What was the amount of actual urine output for the shift? For a Belleville spring the load is applied on _____ Element boundaries are defined when nodal points are connected by unique polynomial curve or surface. After determining the stresses in orthotropic materials by using an appropriate failure theory we can find factor of safety. Stress- strain law defined as ______ A. thermoset. d) N3=1-- Answer: a with transparent plastics? C. firm fit. The geometry has been discretized as shown in Figure 1. d) Element stiffness matrix Lower order polynomials are chosen as shape functions. Answer: b The force and displacement along the y-direction can be correlated using the stiffness k_{yy}=\frac{Eb^3t}{4L^3}. d) =EBq radiography are most effective finding defects For this object first element stiffness matrix is as given. In other words, we need to determine if we can lump the entire structure as a single point in space or if we need to resolve it in one, two, or even three dimensions to get more details of spatial variation in certain quantities of interest. Which is not an advantage of dry fiber composite procedures? a) Dimensions a) Shear strains Answer: d Designing for part stiffness through geometric controls is one of these important tools. a) X direction repairing laminated fiberglass structures is to remove The stiffness of the spring is defined as, (2) Thus each node has two degrees of freedom. Answer: c https://quizack.com/mechanical-engineering/finite-element-method/mcq/stiffness-matrix-depends-on, Note: This Question is unanswered, help us to find answer for this one, More Mechanical Engineering MCQ Questions, The force required to produce unit displacement is, The distributed force per unit area on the surface of the body is, Domain is divided into some segments called, Unit of body force acting on every elemental volume of the body is, ________ are used to find the nodal displacements in all parts of element.

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