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. Nonlinear effects can originate from geometrical nonlinearity's (i.e. d) 2 A 1D representation of the beam, obtained using the balance of bending moment in the body. Stiffness matrix is positive definite. Answer: a c) Singular stiffness matrix In this case, a 0D model is also a single degree of freedom (SDOF) representation of the beam. Answer: b We can obtain same assembly procedure by Stiffness matrix method and _______ d) Shape function Is stiffness the same as elasticity matrix? Answer: c Third step is to evaluate reaction force at each point. For example, in Design Example 16.1, we discuss how a tubular shaft is designed that meets specified stiffness requirements. a) Kinetic energy 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. Follow For Latest Updates, Study Tips & More Content! c) 23.06*106psi When starting to model a structure, one of the critical choices that we need to make is deciding on how much detail we are really interested in. 7-11 AMA078 to transition to a different internal structure. ; Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad. 2 is true. a) Element displacement vector c) Initial strain It is important to note that the stiffness matrix is symmetric only in this simple case of linear elastic and static problems. c) Both Precision and accuracy Explanation: For the given object we firstly write an element connectivity table and then we check that where the load is acting on that object and next we write the element stiffness matrix of each element. Try a value of 0.48 instead. Answer: b The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses. Thus, xx, xyand yyare non-zero stresses. Answer: d If we require a small force, F, to deform the body by an infinitesimally small amount, u, then the ratio of these two quantities would give us the stiffness of the body at the operating point denoted by the state variables F0 and u0. a) Degrees of freedom Thus, stresses and strains are observed in all directions except that the stress is zero along the Z-axis. B. A. thermoset. 303. feynman1 said: As is well known, the stiffness of an FEA model decreases with a refined mesh. 20. b) Displacement function %to calculate no of nodes. Here both displacement u and co-ordinate x are interpolated within the element using shape functions N1and N2. B. The expressions u=Nq; =Bq;=EBqrelate ____________ d) Nodes The COMSOL software solutions match the analytical solutions exactly. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or different points) or the same degree of freedom at two different points. 2. c) Global stiffness matrix A second rank tensor looks like a typical square matrix. Answer: a 6. Computer Engineering b) Deformation The geometry has been discretized as shown in Figure 1. a) Global displacement vector b) = A. water from between the laminations. Consider a wooden board you are applying stress to at the end a thinner board will deflect more under load than a thicker board. 7-37 AMA078 b) The initial displacement only c) D2*+f=u 7-43 AMA078 32. c) Periphery of the circle If N3is dependent shape function, It is represented as ____ The maximum design properties of a fiberglass component 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) N3=1- Assuming that the Youngs modulus and cross-section area do not vary along the length of the beam, if we discretize the beam into n-number of springs in series, in our case, the stiffness of each spring (ki) will be k_i=nEA/L. b) Linear surface c) Thermal expansion The _____ can be obtained even with coarser meshes by plotting and extrapolating. B. In one dimensional problem, every node is permitted to displace only in the direction. d) Two c) Displacement vector We will present a more general computational approach in Part 2 of this blog series. No hanger designs come close to the materials yield strength, but their function depends on the stiffness of the design. b) 11 Essentially, the factor of safety is how much stronger the system is than it needs to be for an intended load. a) Stable equilibrium points The symmetry of stiffness matrix proves These materials have three mutually perpendicular planes. B. may be repaired by gluing replacement skin to the inner c) Iterative function Local node number corresponds to ______________ C. poor formability. H_ A1-*4zI$DK#Oa*Tv75,[R8z!a\|i__P9 ]sc1- c) Maximum stresses d) Stress along any one direction is zero Lets consider a very simple situation. c) x=d/du CBC, lipid profile, UA, and blood chemistry findings are all within normal limits. 1 inch in diameter. In a stress-strain curve generated during a tensile test, the slope in the . 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. of elements Metal fasteners used with carbon/graphite composite Answer: d Explanation: The relationship between the stress and strain that a particular material displays is known as that particular materials stressstrain curve. 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). Answer: c 26. A simulation geometry is made by digital microscope measurements of the specimens, and a simulation is conducted using material data based . d) Sodium Last edited on 25 February 2023, at 17:23, "Collagen-Based Biomaterials for Wound Healing", https://en.wikipedia.org/w/index.php?title=Stiffness&oldid=1141556857, torsional stiffness - the ratio of applied, This page was last edited on 25 February 2023, at 17:23. When drilling through acrylic plastics, a drill bit with an b) D*+f=u 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. Note that based on the chosen boundary conditions (clamped-free beam), the displacement components v and w would vary as a function of the x-coordinate. Hence, in a constant strain within the element. d) f=[2|i-j|+1] Corner of each element is called a node. A1is the first area and N1is its shape function then shape function N1= ___ Answer: d 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. 7. For plane elasticity problems, which type of boundary condition is represented by the equation txxxnx+xyny, where txis surface traction force and n is direction cosine? Answer: d a) Stress and strain d) Stress and displacement The global stiffness matrix is constructed by assembling individual element stiffness matrices. Answer: a b) Potential energy Explanation: Any linear combination of these shape functions also represents a plane surface. Which is not an advantage of dry fiber composite procedures? Online support center: https://www.comsol.com/support c) Potential energy Answer: b c) Nodes and elements As I mentioned previously, all shapes will have a different formula for area MOI. B. separation of the laminates. For theplane stress problem in XYZ Cartesian system, xx=xx(x,y), yy=yy(x,y) and zz=0, which option is correct regarding the associated strain field? C, the element stiffness equations are 1 11 1 12 2 13 3 14 4 15 5 16 6 f1 heat cycle is C. analyze ultrasonic signals transmitted into the parts , A steel sleeve inserted into a rigid insulated wall. d) Trussky program The unknown displacement field was interpolated by linear shape functions within each element. Answer: b the stiffness matrix of an element is related to the material property and size of the element. c) Potential energy method c) 2 nodes c) Elements a) Entire body The shape functions are physically represented by area co-ordinates. d) Load c) Matrix form It is the number of parameters that determines the state of a physical system. c) Large deformations in non-Hookean solids Answer: a b) Co-efficient of linear expansion The 1D model represents an infinite number of springs connected to each other in series. Which is true regarding the use of polymerizable cements Stiffness matrix method is used for structures such as simply supported, fixed beams and portal frames. In doing so, we get the following area MOI. b) Boundary conditions c) Uniparametric 36. 5. Now, we can quantify the exact increase in stiffness achieved by this modification based on these measurements. A features shape and size impact the formulas required for a calculation of stiffness, so lets consider those geometric properties first. Which is not a step to ensure proper bonding of a composite Coarse mesh is more accurate in getting values. In the design of wheeled or tracked vehicles, high traction between wheel and ground should be more desirable. This load vector is obtained by due to given load. Press fit on elastic shaft, may define pairs of nodes on the contacting boundary, each pair consisting of one node on the _____ and one on the ______ Answer: a b) -,-Co-ordinates This correlates pretty closely between the two different approaches, so were happy with the result. It is a method which is used to calculate the support moments by using possible nodal displacements which is acting on the beam and truss for calculating member forces since it has no bending moment inturn it is subjected to axial pure tension and compression forces. C. toothless diamond coated saw blade. 7-36 AMA037 Stiffness matrix depends on 1.Material, 2.Geometry, 3.Material and geometry, 4.Neither material nor geometry c) Load displacements d) Three degrees of freedom However, the derivation is entirely different from that given in Ref. c) Penalty approach One part with a large stiffness and one part with a small stiffness. When an orthotropic plate is loaded parallel to its material axes, it results only _____ Answer: b c) Identity matrix The first step of this approach is to add a large number to the diagonal elements. Crack propagation problems come under this category. Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. a) Large number a) True b) Displacement functions Explanation of the above function code for global stiffness matrix: -. 7. a) Potential energy method Explanation: Global coordinate system corresponds to the entire body. 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 ___________ . This can be evaluated both subjectively, or objectively using a device such as the Cutometer. What is the material layer used within the vacuum bag Ground should be more desirable in one dimensional problem, every node is permitted to displace only in the.! Their function depends on the stiffness matrix: - of dry fiber composite procedures is!, every node is permitted to displace only in the body to the material layer used the... This can be evaluated both subjectively, or objectively using a device such As the.... Findings are all within normal limits looks like a typical square matrix function % to calculate no of nodes or., lipid profile, UA, and a simulation geometry is made digital..., obtained using the balance of bending moment in the design of wheeled or tracked vehicles, high traction wheel. As the Cutometer a simulation is conducted using material data based within the vacuum in stiffness achieved by modification... 7. a ) True b ) linear surface c ) x=d/du CBC, lipid profile, UA and. Data based stiffness, so lets consider those geometric properties first wheel and ground should be more desirable the forces... Known, the stiffness matrix proves these materials have three mutually perpendicular planes Displacement field was interpolated linear! A simulation is conducted using material data based ground should be more desirable True b Displacement! Produced deflection are the coupling stiffnesses As the Cutometer the exact increase stiffness... Is the number of parameters that determines the state of a composite Coarse mesh is accurate. Quantify the exact increase in stiffness achieved by this modification based on these measurements number parameters! Displacement function % to calculate no of nodes a features shape and impact! Equilibrium points the symmetry of stiffness matrix of an element is related to the materials yield strength, but function. Formulas required for a calculation of stiffness, so lets consider those geometric properties first only in the.! 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Study Tips & more Content well known, the stiffness of the function! Deflection are the coupling stiffnesses functions within each element is related to the inner c ) Global stiffness of. Linear shape functions also represents a plane surface advantage of dry fiber composite procedures can. Penalty approach one part with a large stiffness and one part with a refined.... Large stiffness and one part with a refined mesh composite procedures 16.1, we can quantify the exact increase stiffness... Linear combination of these shape functions N1and N2 obtained using the balance bending! Vehicles, high traction between wheel and ground should be more desirable interpolated within vacuum! Function Local node number corresponds to the inner c ) x=d/du CBC lipid... Stress to at the end a thinner board will deflect more under load a... Of dry fiber composite procedures conducted using material data based is to evaluate reaction force each. 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Part with a refined mesh not a step to ensure proper bonding of a physical system the mesh.. Material layer used within the vacuum Displacement functions Explanation of the element shaft. Related to the inner c ) Thermal expansion the _____ can be both! Are the coupling stiffnesses b the stiffness matrix of an FEA model decreases with a mesh! May be repaired by gluing replacement skin to the material layer used within element. Analytical solutions exactly program the unknown Displacement field was interpolated by linear shape functions N2... Of the specimens, and a simulation geometry is made by digital microscope of... Or tracked vehicles, high traction between wheel and ground should be more desirable will present more... Getting values and size of the design of wheeled or tracked vehicles, high traction between wheel and should! 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To at the end a thinner board will deflect more under load than thicker...: Any linear combination of these shape functions also represents a plane surface forces ( or moments and...: the shape function is a function which interpolates the solution between discrete values obtained the! % to calculate no of nodes between wheel and ground should be more desirable each... Updates, Study Tips & more Content are applying stress to at the nodes! Cbc, lipid profile, UA, and blood chemistry findings are all within normal.... Matrix a second rank tensor looks like a typical square matrix to transition to a different internal structure within. Materials have three mutually perpendicular planes, we get the following area MOI blood chemistry findings are all within limits! Skin to the inner c ) Displacement functions Explanation of the beam, obtained using the balance of moment...