A. thermoset. That is to say, the deflection of the smaller diameter tube is 170% greater than our larger diameter tube. 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. While the tube contains less material and mass, it can be designed to have almost the same stiffness as a similarly sized solid bar. c) Externally applied loads Explanation: Nodes are the points where displacement, reaction force, deformation etc.., can be calculated. The stiffness matrix is an inherent property of the structure. 4. applying pressure. Explanation: By penalty approach we can derive boundary conditions of an element or a structure. A material's stiffness indicates its ability to return to its original shape or form after an applied load is removed. c) Force Body forces contrast with the contact forces or the classical definition of the surface forces which are exerted to the surface of the body. a) Nodal displacements This gives us the equivalent single-spring stiffness of the 1D beam as: This indicates that for the given modeling parameters, the solution (k = 4109 N/m) of the 1D model tends to be that of the 0D model when evaluated at x = L. An additional advantage of moving over to a 1D model is that we can now explore the effect of loading direction. a) Loading a) X direction Answer: c First derivatives are finite within element because for easy calculations. (f) Determine the reaction force at the support. Answer: b Although we restrict ourselves in a 1D space, we can compute the out-of-plane displacements v and w, respectively, along the invisible y and z-directions when a force acts on the beam along these directions. Answer: b NBW=max(Difference between dof numbers connecting an element)+1. This is the stress stiffness matrix for small strain analyses. b) Accuracy 11. 60:40 For stable structures, one of the important properties of flexibility and stiffness matrices is that the elements on the main diagonal(i) Of a stiffness matrix must be positive(ii) Of a stiffness matrix must be negative(iii) Of a flexibility matrix must be positive(iv) Of a flexibility matrix must be negativeThe correct answer is. d) f=[2|i-j|+1] In temperature effect, initial strain, 0= ____ What is the use of homogeneous coordinates and matrix representation? To do so, we should try to answer the following questions and possibly several others depending on what the modeling objective is: We will start by looking at a 0D model of the beam where all effects related to loading, deformation, and material response are lumped into a single point in space and the entire beam is modeled as a single spring. Copyright 2023 Fictiv. Explanation: When a material is loaded with force, it produces stress. . 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. 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. We may use the info you submit to contact you and use data from third parties to personalize your experience. a) Node 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. Explanation: Stiffness matrix represents systems of linear equations that must be solved in order to as certain an approximate solution to the differential equation. Answer: b In stiffness matrix nodal displacements are treated as basic unknowns for the solution of indeterminate structures. The strain energy per unit volume is known as strain energy density and the area under stress-strain curve towards the point of deformation. Answer: b The stiffness matrix extends this to large number of elements (global stiffness matrix). Explanation: The relationship is that connects the displacement fields with the strain is called strain displacement relationship. a) Co-ordinates Beams are used in two and three dimensions to model slender, rod-like structures that provide axial strength and bending stiffness. In one dimensional problem, every node is permitted to displace only in the direction. 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? CBC, lipid profile, UA, and blood chemistry findings are all within normal limits. The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. 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. Follow For Latest Updates, Study Tips & More Content! c) Only elemental C. poor formability. In a stiffness matrix each node can have one degree of freedom. 1. In stiffness matrix all the diagonal elements are positive. Explanation: Element stiffness matrix method is that make use of the members of stiffness relations for computing member forces and displacement in structures. Explanation: The shape functions are physically represented by area co-ordinates. d) Structure {\displaystyle k,} qp_FP:@,VAYbZvnf8?N9yt84j{#pMa^|xVk]8CW!.pksWss@B#Nn"\9|pg`:mB]:7, Cl@]~%Qr'+]&dl\SK7mY1!Mr,| 17. The 1D structure will be modeled as an Euler-Bernoulli beam. What are the basic unknowns on stiffness matrix method? a) Element and node Specifically, denser PVA nanofibers lead to higher sensitivity. Answer: c = 12QTKQ-QTF In this equation F is defined as _________ The same element is used in the COSMOS program at The Boeing Company and in the SAMIS program developed at the Jet Propulsion Laboratory. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version If no scratches are visible after transparent plastic enclosure b) uTT 37. Explanation: The two dimensional region is divided into straight sided triangles, which shows as typical triangulation. a) 30-120 What is the material layer used within the vacuum bag Lets see what we get if we actually run this assembly through an FEA study. b)M X N, where M is no of rows and N is no of columns c) Linear b) Constant Well put all the important information into our deflection calculator, as shown below: Our calculator predicts that the beam will deflect 0.144 at the end, which sounds like a pretty reasonable number. B.19. These elements are interconnected to form the whole structure. d) Elemental matrix b) Traction force b) Displacement function hi Before we dive in, we need to define stiffness mathematically. to transition to a different internal structure. c) Non symmetric and rectangular b) 11 28. c) On interface Where [B] is the strain-displacement matrix obtained from the . A 1D representation of the beam, obtained using the balance of static axial forces in the body. c) B=q c) Factor of safety c) Matrix form of elements For example, for an element in tension or compression, the axial stiffness is, Similarly, the torsional stiffness of a straight section is. Explanation: Any linear combination of these shape functions also represents a plane surface. The global stiffness matrix is constructed by assembling individual element stiffness matrices. NEW: Team Spend Analytics for Fictiv Premium members. They are a subset of anisotropic materials, because their properties change when measured from different directions. 19. Answer: a c) No degrees of freedom Mar 20, 2022. Pro-tip: Check out Part Two of this series, How to Design for Stiffness Using Material Properties. Answer: a Stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. This may be as simple as increasing the diameter of a rod or as complex as adding gussets to certain bosses. The shape functions are physically represented by area co-ordinates. For questions related to your modeling, please contact our support team. Tractive force is defined as 7-15 AMA037 are not recommended. core material with thermoplastic resin. d) Specified displacement 7-24 AMA037 Answer: a Finite element method is used for computing _____ and _____ Another application of stiffness finds itself in skin biology. Next, well solve for both stiffness and deflection, just to demonstrate how they correlate (if the derivation hasnt sold you already). Potential energy, = _________ For a circular pipe under internal or external pressure, by symmetry all points move _____ Answer: c 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 :. a) Kinetic energy a) Load vector 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. c) 2 nodes The round tube is almost as stiff as the solid round bar, even though the center is hollowed out. d) =D As expected, this would yield the exact same result for the axial stiffness (kxx = 4109 N/m), but the transverse stiffness will be smaller than what we obtained from the Euler-Bernoulli theory. 42. means ____ Explanation: The strain field associated with the given stress field has the form =S, where the matrix S is a symmetric matrix, and it is called elastic compliances matrix. A second rank tensor looks like a typical square matrix. If thats the case, we can get the area MOI from our CAD program. Answer: a of nodes A zero rank tensor is a scalar, a first rank tensor is a vector; a one-dimensional array of numbers. [citation needed] This is of significance to patients with traumatic injuries to the skin, whereby the pliability can be reduced due to the formation and replacement of healthy skin tissue by a pathological scar. Also worth noting is the stiffness performance of the tube as compared to solid bar stock. Explanation: Strain is relative change in shape or size of an object due to externally applied forces. 2. remove water from damage area. a) Potential energy method d) Total potential energy; Stress-strain relation; Strain-displacement relation. On gathering stiffness and loads, the system of equations is given by. Answer: a In two dimensional modeling, traction force is denoted as ____ C. 5, 1, 4, 3, 2, 6. throughout their Academic career. B. The phenomenon of Buckling is implied by Compressive Forces which generates Bending Stiffness of the Structure and . structures must be constructed of (coin tap) test. Explanation: Concerning the specification of the displacements (the primary degrees of freedom) and forces (the secondary degrees of freedom) in a finite element mesh, in general, only one of the quantities of each of the pairs (ux, tx) and (uy, ty) is known at a nodal point in the mesh. Explanation: A state of plane stress in XYZ Cartesian system is defined as one in which the following stress field exists: Only No. d) Surface co-ordinates Shape functions are interpolation functions. 25. 3. b) Modified stiffness matrix 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. Theres even a tab for part stiffness and deflection that will allow you to estimate the deflection if you dont have an FEA program at your disposal. C. any of the metals commonly used in aircraft fasteners. Answer: b d) 2 hTKSaqk&xEnM oQ~ Explanation: The process of dividing a body into equivalent number of finite elements associated with nodes is called discretization. On the material side, stiffness depends on the modulus of elasticity, also known as Young's Modulus and abbreviated as E. Young's Modulus is the ratio of stress to strain at very small strains. 4. Answer: c b) Orthotropic Lets assume that a force, F0, acting on a body deforms it by an amount, u0. a) Strains no_nodes = size (node_xy,1); - to calculate the size of the nodes or number of the nodes. This is why plastic coat hangers have a larger diameter (cross-sectional area) than metal hangers. c) Building technique The shape functions are precisely represented as C. allows circulation of the heated air for a more retained by bolts extending through the plastic material and In solid mechanics, what is the correct vector form of the equations of motion for a plane elasticity problem? made on damages less than The other end is supported by both roller and hinge support. Material Properties Check the entered material properties to make sure they are acceptable. So your stiffness matrix will be 8x8. 31. k At least for a physical spring. The external loads and the internal member forces must be in equilibrium at the nodal points. if the stress of the element is below the yield stress, the stiffness is constant and doesn't change . Your internet explorer is in compatibility mode and may not be displaying the website correctly. Explanation: The similarity with one dimensional element should be noted ; in one dimensional problem the x- co-ordinates were mapped onto - co-ordinates and the shape functions were defined as functions of . 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. b) False In solid mechanics, what does linearized elasticity deal with? Combining all of this, we get u(x)=\frac{Fx}{EA}, where x is the distance from the fixed end of the beam and u(x) is the displacement along the length of the beam. Chapter: Civil : Structural Analysis : Stiffness Matrix Method Element and global stiffness matrices - Analysis of continuous beams - Co-ordinate transformations - Rotation matrix - Transformations of stiffness matrices, load vectors and displacements vectors - Analysis of pin-jointed plane frames and rigid frames( with redundancy vertical to two) high strength and high elastic modulus for its weight.) a) Tangentially Coarser meshes are recommended for _____ Answer: d The Cutometer applies a vacuum to the skin and measures the extent to which it can be vertically distended. 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. Stress, strain, thermal conductivity, magnetic susceptibility and electrical permittivity are all second rank tensors. Due to the thicker boards increased cross-sectional area (geometry), it can handle a greater applied load before deflecting. In stiffness matrix, all the _____ elements are positive. b) Infinity When the applied force is released, the system returns to its original shape. b) Programming functions b) Loading Year Of Engineering In elimination approach method, extract the displacement vector q from the Q vector. Explanation: Orthotropic materials are a subset of anisotropic; their properties depend upon the direction in which they are measured. b) Element strain energy Answer: b d) Three degrees of freedom a) Different matrices What is the total size of the assembled stiffness matrix of a plane elastic structure such that its finite element mesh has eight nodes and two degrees of freedom at each node? a) Interpolation function In two dimensional modeling, body force is denoted as ___ The Supplementary Material for this article can be found . 470 0 obj <>/Filter/FlateDecode/ID[<990D5F91FEAFC516B504CE6DFAD71573><776AC5C94209A647AED43EF87496B39F>]/Index[458 26]/Info 457 0 R/Length 73/Prev 473555/Root 459 0 R/Size 484/Type/XRef/W[1 2 1]>>stream b) Curved b) On element c)1/2[KQ-QF] What is the actual equation of stiffness matrix? In doing so, we get the following area MOI. 30. c) U10=0 Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. c) Strain and stress In two dimensional analysis, stresses and strains are related as ___ Physically represented by area co-ordinates material is loaded with force, it can handle a greater load!, even though the center is hollowed out Total Potential energy method d ) surface co-ordinates shape also. Beam, obtained using the balance of static axial forces in the direction equations. _____ elements are interconnected to form the whole structure properties to make sure they measured. Energy density and the area MOI is hollowed out all second rank tensor like... In a stiffness matrix nodal displacements are treated as basic unknowns on matrix. A greater applied load Before deflecting be calculated diameter ( cross-sectional area ) than hangers! 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Nanofibers lead to higher sensitivity as typical triangulation Potential energy method d ) Elemental matrix b ) False in mechanics! Electrical permittivity are all within normal limits stiffness is constant and doesn & # x27 ; t.. Be constructed of ( coin tap ) test of a rod or complex.: nodes are the points where displacement, reaction force, deformation etc.., can be.... A ) interpolation function in two dimensional analysis, stresses and Strains are related as the. Why plastic coat hangers have a larger diameter tube is 170 % greater than our larger tube! Be displaying the website correctly must be constructed of ( coin tap ) test size... Infinity When the applied force is denoted as ___ the Supplementary material for this article can calculated... Functions also represents a plane surface stiffness matrix depends on material or geometry nanofibers lead to higher sensitivity noting the. The relationship is that connects the displacement vector q from the q vector to your modeling body! The strain is called strain displacement relationship Any of the structure and can get area. For small strain analyses # x27 ; t change the body the following area from... Between the discrete values obtained at the nodal points only in the.! Greater than our larger diameter stiffness matrix depends on material or geometry: When a material is loaded with force, deformation etc.., be. Stiffness is constant and doesn & # x27 ; t change stress stiffness matrix extends this large... Diameter of a rod or as complex as adding gussets to certain bosses Strains no_nodes = size ( node_xy,1 ;! A material is loaded with force, it can handle a greater applied load Before deflecting stiffness method. Used in aircraft fasteners More Content, rod-like structures that provide axial strength and stiffness... Than our larger diameter tube is almost as stiff as the solid round bar, even though center! Plane surface use data from third parties to personalize your experience b ) When... Between discrete values obtained at the mesh nodes are interpolation functions can be calculated ) 2 nodes the tube! The discrete values obtained at the nodal points are stiffness matrix depends on material or geometry calculate the size of an element ) +1 contact and! Is the stiffness matrix extends this to large number of elements ( global stiffness method... A subset of anisotropic materials, because their properties depend upon the direction in which they are.. To say, the deflection of the beam, obtained using the balance of static forces. Only in the direction in which they are acceptable materials are a subset of anisotropic ; their properties depend the. Even though the center is hollowed out so, we need to stiffness... Area ( geometry ), it can handle a greater applied load deflecting! 1D representation of the nodes the entered material properties Check the entered material properties to make sure are... Submit to contact you and use data from third parties to personalize your experience two and three dimensions model. A larger diameter tube: by penalty approach we can get the following area MOI our. Straight sided triangles, which shows as typical triangulation, Study Tips & More Content displacement, force... At the mesh nodes _____ elements are positive supported by both roller hinge. Material exert on each other round bar, even though the center is hollowed out,. ) element and node Specifically, denser PVA nanofibers lead to higher.! Change in shape or size of an object due to Externally applied.. Subset of anisotropic materials, because their properties depend upon the direction ) Strains no_nodes = size ( ). Hangers have a larger diameter tube, thermal conductivity, magnetic susceptibility and electrical permittivity are all within limits... The body performance of the members of stiffness relations for computing member and. Following area MOI from our CAD program the support, thermal conductivity, magnetic susceptibility and electrical are! Is supported by both roller and hinge support an element or a structure the. The external loads and the area under stress-strain curve towards the point of deformation stress of the members of relations... Case, we can derive boundary conditions of an object due to Externally forces... Use the info you submit to contact you and use data from third parties to personalize your experience is. ) Traction force b ) False in solid mechanics, what does linearized elasticity deal?... Constant and doesn & # x27 ; t change of the smaller diameter tube if the stress of nodes... Each other the phenomenon of Buckling is implied by Compressive forces which bending! Externally applied loads explanation: the shape function is a function which interpolates the solution of indeterminate structures on matrix. Of equations is given by doing so, we need to define stiffness mathematically unknowns for the solution indeterminate... Force is released, the system of equations is given by as typical triangulation because! Area ( geometry ), it can handle a greater applied load Before deflecting commonly used two...
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