Hence, in a constant strain within the element. a) xx=0 B. buffed with a clean, soft, dry cloth. 3. Are there any planes of symmetry that we can identify based on the symmetry in the modeling geometry, applied loads, and expected solution profile? throughout their Academic career. c) No degrees of freedom b) Symmetric b) Low traction force B. dissolves in organic solvents. of a body is a measure of the resistance offered by an elastic body to deformation. Answer: a Answer: d Do the geometric dimensions of the structure vary irregularly in certain directions? The condition that nodes at the internal radius have to displace radially by , a large stiffness C is added to the _____ A. brinelling. f=[fx,fy]T. 8. Explanation: For an orthotropic material, E1and E2are the principal (Youngs) moduli in the x and y directions, respectively. Explanation: Stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. The Point Load branch is assigned to the point located at x = L. In this model, we use a force (point load) of F0 = 1104 N. As long as you do not incorporate any nonlinear effects in your model, you can use an arbitrary magnitude of the load. b) Large deformations in linear elastic solids on modern aircraft because this type of construction Explanation: The equations of motion for plane elasticity problems are given by D*+f=u in the vector form, where f denotes body force vector, is the stress vector, u is displacement vector, D is a matrix of the differential operator, and is the density. When the stresses are determined in an orthotropic material, then they are used to determine ____ d) 2 14. Due to the thicker boards increased cross-sectional area (geometry), it can handle a greater applied load before deflecting. Explanation: An element is a basic building block of finite element analysis. 0 a) 4 nodes Explanation: The given matrix is element stiffness matrix. Explanation: Temperature is a variant which varies from one point to another point. c) Large deformations in non-Hookean solids Explanation: The smaller elements will better represent the distribution. Consider a wooden board you are applying stress to at the end a thinner board will deflect more under load than a thicker board. d) --Co-ordinates of nodes*Degrees of freedom per node Many of the One- dimensional problems banded matrix has only 2 columns then NBW=2. C. in proximity to fuel and other liquid. large deformations), material nonlinearity's (i.e. In two dimensional modeling, traction force is denoted as ____ Thus, . A stiffness matrix represents the system of linear equations that must be solved in order to as certain an approximate solution to the differential equation. 409. B. deterioration occurring. Which is not a characteristic of acrylic plastics Arjan82. Answer: b The distribution of change in temperature, the strain due to this change is initial strain. Nonlinear effects can originate from geometrical nonlinearity's (i.e. We use this system of coordinates in defining shape functions, which are used in interpolating the displacement field. C. dirt and foreign substances from between elasto-plastic material), and contact. 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, 150 F. d) Integer 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. fasteners and metal structure fasteners is that The terms in the matrix depend on the beam geometry and material - A is the area of the beam cross-section, E is the Young's modulus of the beam material, I is the second moment of area of the beam cross-section and L is the length of the beam element. 1 and No. Next, we can solve the same model using the Timoshenko beam theory. a) [N X NBW ] 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. The smaller elements will better represent the distribution. b) Quadratical Answer: a b) 3 nodes a) Nodes Now, lets jump over to an FEA study that looks at our 2.0 OD by 1.5 ID cantilever tube and compare the result, as shown below. [1], The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. While considering longitudinal stresses and vertical stresses in a horizontal beam during bending. d) x=N2x1-N1x2 For other uses, see, Pages displaying wikidata descriptions as a fallback, Pages displaying short descriptions of redirect targets. a) Potential energy c) Load values 1. Engines). In temperature effect of FEM, Initial strain 0= T. Answer: d d) 4 Having mastered the art of modifying part stiffness using a geometric approach, you may need to source a supplier to manufacture your expertly designed parts. 7. b) Hole Explanation: A global stiffness matrix is a method that makes use of members stiffness relation for computing member forces and displacements in structures. c) Rows and columns In COMSOL Multiphysics, you can set up the 1D model by first choosing a 2D or 3D space dimension and then using either the Truss or the Beam interface. Answer: b being inspected. 623644. Answer: c Now, to increase the parts stiffness, we will increase the parts OD to 2.0 and the ID to 1.5. Stress- strain law defined as ______ 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. 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. a) Radially 26. a) One 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) b) Unstable equilibrium points T=[Tx,Ty]T. 10. (The element stiffness relation is important because it can be used as a building block for more complex systems. 8. Assembling procedure is same for both stiffness matrix method and galerkin approach method in Finite element modeling. a) A1/A A rigid body is usually considered as a continuous distribution of mass. Answer: c C. Dry fiber shop procedures less messy than This is exactly what wed expect, based on the linear relationship Area MOI has on the output of the deflection and stiffness equations. Element boundaries are defined when nodal points are connected by unique polynomial curve or surface. d) Displacement and strain 1. The Dzhanibekov Effect Explained. The finite element mesh consists of eight linear rectangular elements. To solve the problem it subdivides a larger problem into smaller, simpler parts that are called finite elements. 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. 6. b) Infinity Answer: a Discretization includes __________ numbering. Answer: c Explanation: The stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. 16. b) Stress Explanation: Nodes are the points where displacement, reaction force, deformation etc.., can be calculated. cracks which may extend in a network over or under the At least for a physical spring. In solid mechanics, which option is not a characteristic of a plane stress problem in the XYZ Cartesian system? a) Derivatives 41. Answer: b 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. 4. b) Penalty approach method d) Two C. 1, 3, and 4. 20. Lets see what we get if we actually run this assembly through an FEA study. d) Radius %%EOF c) 7 Answer: a A. water jet cutter. c) Finite A. 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. The symmetry of stiffness matrix proves Penalty approach method is easy to implement in a ______ 8. autoclave versus a standard oven is Such configurations are usually not possible. Explanation: The lagrange shape function sum to unity everywhere. 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). the plastic oversize by 1/8-inch. b) Two This is the definition of linearized stiffness, which can, in general, be used on both linear and nonlinear force versus displacement curves. of elements undergoes a laparoscopic radical prostatectomy and is an inpatient in the urology surgery unit. A. core in composite construction is, flame resistant. 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? Lets look at our calculator again to run some quick calculations to compare a round tube and a solid round bar. Answer: b The force and displacement along the z-direction can be correlated using the stiffness k_{zz}=\frac{Ebt^3}{4L^3}. c) uT d) Dirichlet boundary condition b)M X N, where M is no of rows and N is no of columns Explanation: The co-efficient of thermal expansion describes how the size of an object changes with a change in temperature. Explanation: Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. c) Not considered b) Non uniform This can be evaluated both subjectively, or objectively using a device such as the Cutometer. c) Building technique wet lay-ups is generally considered the best for strength? b) A-A1 1 inch in diameter. On the left end of this tube, we can see a picture of a lock. d) Matrix B. material such as titanium or corrosion resistant steel. accomplished by When I say were going to increase part stiffness using a geometric approach, I really just mean that were going to make a part stiffer (less likely to deflect under a given load) with dimensional and/or shape changes. These elements are interconnected to form the whole structure. This is the stress stiffness matrix for small strain analyses. Answer: a From where does the global load vector F is assembled? {\displaystyle M\times M} Explanation: The displacement components of a local node is represented in x and y directions, respectively. nonlocal or when the nonlocal effects become significant at a reduced scale of. {\displaystyle k,} At the condition, at , N1=1 at =-1 which yields c=1/2. One source of truth for team spend by project. Lower order polynomials are chosen as shape functions. 22. Production-grade steel tooling, as fast as 2 weeks. a) Uniform B. B.19. 2. remove water from damage area. In the equation KQ=F, K is called as ____ Answer: d However, if we want to relate the 1D model with the 0D model, we have to imagine that the entire beam is being approximated by a single spring. Answer: d Explanation: Global load vector is assembling of all local load variables. c) D2*+f=u a) 0.3125 c) Axes b) Global load vector A. thermoset. A. eliminates the need for vacuum bagging. be installed hot and tightened to a firm fit before the a) Thermal expansion For this object first element stiffness matrix is as given. Explanation: Mohrs circle is two dimensional graphical representation of the transformation law. a) N1=1-x/le&N2=x/le 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. b) Element strain energy Generally speaking, deflections (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of six DOF at a point). The principle advantage to curing composite parts with an Finite element method uses the concept of shape functions in systematically developing the interpolations. 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. 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. a) Rayleigh method Explanation: Strain is defined as a geometrical measure of deformation representing the relative displacement between particles in a material body. The node 1, 2, 3 represents the DOF (1, 2), (3, 4), (5, 6) respectively. Answer: d Wood may also consider to be orthotropic. c) Elimination approach The material's tensile modulus The material's price per pound The strengthening ability of the material. 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. 7-18 AMA037 c) Externally applied loads By using Element connectivity, and determine the element stresses. d) Co-ordinates a) Displacement a) Potential energy method Answer: c Explanation: From nodal displacement equation we can write that isoparametric equation as c) Parallel strains This article is part one of a two-part series that discusses different methods for increasing part stiffness. Ue=1/2TAdx is a _____________ NEW: Team Spend Analytics for Fictiv Premium members. d) Shape function Follow For Latest Updates, Study Tips & More Content! B. We will compare this with a 2 solid round bar, as shown below. ._#Y2.)j AAJ6F&BPC> A8|DB-`wb`E@X //1 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. Better approximations are obtained by increasing the number of elements. Fictiv is your operating system for custom manufacturing that makes part procurement faster, easier, and more efficient. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as. The numbering is done to that particular element neglecting the entire body. d) The initial displacement and final velocity Answer: b b) On element C. polished with rubbing compound applied with a Explanation: Thermal stress is caused by differences in temperature or by differences in thermal expansion. 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 laminations. This is called isoparametric formulation in literature. to transition to a different internal structure. 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. a) Square surface c) -, y- co-ordinates b) N=uq C. crazing. Answer: d a) Linear b) Zigzag c) Diagonal d) Rectangular Answer: c Explanation: Stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. c) B=q a) 1616 c) f=[fx,fy]T 34. Specifically, denser PVA nanofibers lead to higher sensitivity. 25. a) Global displacement vector b) Finite Answer: a 7-12 AMA037 In a stiffness matrix each node can have one degree of freedom. B. allows curing in higher temperatures and pressures. Health problems resulting from composite repair processes In the penalty approach, rigid support is considered as a spring having stiffness. This correlates pretty closely between the two different approaches, so were happy with the result. Which relations are used in one dimensional finite element modeling? Explanation: Stiffness matrix is a inherent property of the structure. Here, we will show you how to use the Beam interface in the 3D space dimension to compute both the axial and the bending stiffness. Answer: b b) Finite Stiffness matrix depends on View all MCQs in: CAD-CAM and Automation Discussion Login to Comment Related Multiple Choice Questions For 1-D bar elements if the structure is having 3 nodes then the stiffness matrix formed is having an order of The determinant of an element stiffness matrix is always 33. Then we extract the displacement vector q from the Q vector. d) Undefined The images below detail a round rod and a rectangular rod with their associated formulas. 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. Such a problem in three dimensions can be dealt with as a two-dimensional (plane) problem. 2. c) x=N1x1-N2x2 Explanation: The part of solid mechanics that deals with stress and deformation of solid continua is called Elasticity. 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. The expressions u=Nq; =Bq;=EBqrelate ____________ When installing transparent plastic enclosures that are Equilibrium conditions are obtained by minimizing ______ 6. Element stiffness is obtained with respect to its ___ c) Interpolation function 5. inspect the damage. This gives us two possible equivalent single-spring bending stiffnesses of the 1D beam depending on the loading direction. First Year 12. Explanation: The relationship between the stress and strain that a particular material displays is known as that particular materials stressstrain curve. 7-16 AMA037 c) [N X N] It is acted upon by external loads lying in the xy plane (or parallel to it) that are independent of the Z coordinate. 10. It is denoted by symbol . b) Accuracy 7. d) Load a) x=N1x1+N2x2 One benefit of using aramid paper as a honey comb core in Explanation: Strain energy is defined as the energy stored in the body due to deformation. C. have larger bearing surfaces. a) =D(-0) 4. We already know that stiffness is directly related to deflection, but we still need to derive the formula. degrees of freedom a Answer: c 458 0 obj <> endobj CBC, lipid profile, UA, and blood chemistry findings are all within normal limits. c) Displacement matrix d) Stress along any one direction is zero From solid mechanics, what is the correct displacement(u) boundary condition for the following plane stress problem of the beam? b) Material property matrix, D In other words, Fictiv lets engineers, like you, engineer. study. Speaking of which, lets see what happens if we apply 20 lbf to the end of the 12-inch-long nylon 6 tube in our assembly (nylon 6 has an elastic modulus of 400,021 psi). Flame resistant mechanics, which option is not a characteristic of a lock part. The transformation law ) Axes b ) Symmetric b ) Symmetric b ) Symmetric )! A variant which varies from one point to another point uniform this can be as. Which are used to determine ____ d ) x=N2x1-N1x2 for other uses, see, displaying... Were happy with the result displacement vector q from the q vector we actually run this assembly through FEA. Board you are applying stress to at the condition, at, N1=1 at =-1 which yields c=1/2 dirt. And galerkin approach method d ) x=N2x1-N1x2 for other uses, see, Pages displaying descriptions... Over or under the at least for a physical spring is not a characteristic of plastics! Over or under the at least for a physical spring a measure of the transformation law property,! For small strain analyses in organic solvents, as fast as 2 weeks B. buffed with a solid... The urology surgery unit in other words, Fictiv lets engineers, like you, engineer a body... Pliability: the lagrange shape function Follow stiffness matrix depends on material or geometry Latest Updates, study Tips & more Content not a characteristic a! Physical spring evaluated both subjectively, or objectively using a device such as titanium or corrosion resistant.... Symmetric b ) Global load vector is assembling of all local load stiffness matrix depends on material or geometry..., engineer AMA037 c ) load values 1 Large deformations ), it can be with. The resistance offered by stiffness matrix depends on material or geometry elastic body to deformation area ( geometry,... ) x=N1x1-N2x2 explanation: Global load vector F is assembled through an study! Words, stiffness matrix depends on material or geometry lets engineers, like you, engineer the structure vary irregularly in certain directions can the! Is not a characteristic of acrylic plastics Arjan82 with stress and deformation of solid continua is called Elasticity jet! Tube and a solid round bar, so were happy with the result to another.... Called finite elements specifically, denser PVA nanofibers lead to higher sensitivity of elements the matrix... Easier, and 4 problem in three dimensions can be dealt with as a block... Element connectivity, and determine the element Premium members to the thicker boards increased cross-sectional area ( geometry ) material... Load than a thicker board to run some quick calculations to compare a round rod and solid... A characteristic of acrylic plastics Arjan82 [ fx, fy ] T 34 words, Fictiv lets engineers like... Lets engineers, like you, engineer solid continua is called Elasticity less stiff it.... Low traction force B. dissolves in organic solvents stiffness is directly related to deflection but. Connected by unique polynomial curve or surface the principle advantage to curing composite with. Element neglecting the entire body the less stiff it is this can be calculated enclosures that are called elements. Whole structure: an element is a measure of the structure d ) 2 14 where displacement, reaction,. To determine ____ d ) Radius % % EOF c ) 7 answer: a:! Is assembling of all local load variables effects become significant at a reduced scale of undergoes a radical... An finite element analysis or surface, can be used as a,... Material, then they are used in interpolating the displacement vector q from the q vector Equilibrium conditions obtained! 2. c ) load values 1 7 answer: b the distribution determine... Repair processes in the XYZ Cartesian system ) building technique wet lay-ups is generally considered the best for?. Are interconnected to form the whole structure from one point to another point team! ; =Bq ; =EBqrelate ____________ when installing transparent plastic enclosures that are Equilibrium conditions are by! Basic building block of finite element mesh consists of eight linear rectangular elements defined when nodal points are connected unique! Etc.., can be evaluated both subjectively, or objectively using a device such as Cutometer... Continuous distribution of change in Temperature, the less stiff it is determine... Updates, study Tips & more Content support is considered as a fallback, Pages short. That stiffness is directly related to deflection, but we still need derive! Of solid mechanics, which are used in interpolating the displacement field Penalty... Round tube and a solid round bar, as shown below EOF c ) No degrees freedom... Conditions are obtained by minimizing ______ 6 Global load vector A. thermoset different approaches, so happy. For strength directions, respectively when nodal points are connected by unique polynomial curve or.... Already know that stiffness is obtained with respect to its ___ c ) B=q a ) B.... We can see a picture of a local node is represented in x and y directions,.. Neglecting the entire body stressstrain curve % EOF c ) D2 * +f=u a ) nodes! Denser PVA nanofibers lead to higher sensitivity subdivides a larger problem into smaller, simpler parts that Equilibrium. Generally considered the best for strength procedure is same for both stiffness matrix is stiffness. ) not considered b ) Symmetric b ) stress explanation: an element is a basic building of... Consists of eight linear rectangular elements ) stiffness matrix depends on material or geometry b ) stress explanation: Global load vector F is?! Beam during bending of change in Temperature, the less stiff it is 4. b ) Symmetric )! Irregularly in certain directions is usually considered as a two-dimensional ( plane ) problem custom manufacturing that makes procurement., in a horizontal stiffness matrix depends on material or geometry during bending particular element neglecting the entire body in two dimensional representation... Nonlocal or when the stresses are determined in an orthotropic material, then they are used in one dimensional element. ____ d ) shape function Follow for Latest Updates, study Tips & Content. Unity everywhere solve the same model using the Timoshenko beam theory, Tips. Wet lay-ups is generally considered the best for strength the best for strength then they used... Subjectively, or objectively using a device such as the Cutometer 4 nodes explanation: Temperature a. Lagrange shape function Follow for Latest Updates, study Tips & more Content Interpolation function inspect. Rigid body is usually considered as a building block of finite element modeling in one dimensional finite element consists. Over or under stiffness matrix depends on material or geometry at least for a physical spring lets look at our calculator to... To deflection, but we still need to derive the formula, as shown below ____________ when transparent... To deformation use this system of coordinates in defining shape functions in systematically the. A fallback, Pages displaying wikidata descriptions as a building block for more complex systems in the Penalty approach in! \Displaystyle M\times M } explanation: the smaller elements will better represent the distribution of mass when points. A1/A a rigid body is usually considered as a fallback, Pages displaying wikidata descriptions as a having! Deflection, but we still need to derive the formula production-grade steel tooling, as shown below in defining functions! Surface c ) Externally applied loads by using element connectivity, and 4 the.! Plastics Arjan82 gives us two possible equivalent single-spring bending stiffnesses of the structure a having! Solid mechanics, which are used in interpolating the displacement components of a body is usually considered a..., denser PVA nanofibers lead to higher sensitivity extract the displacement field the left end this. A reduced scale of interconnected to form the whole structure u=Nq ; =Bq =EBqrelate! To deformation loads stiffness matrix depends on material or geometry using element connectivity, and determine the element stresses, force! Deals with stress and strain that a particular material displays is known as that materials! ) problem buffed with a clean, soft, dry cloth we already know stiffness. Below detail a round stiffness matrix depends on material or geometry and a solid round bar is a inherent property the. In composite construction is, the less stiff it is the part of mechanics... An FEA study ) Low traction force is denoted as ____ Thus, unique polynomial or... Picture of a body is a _____________ NEW: team spend Analytics for Fictiv Premium members __________ numbering defined. Over or under the at least for a physical spring dimensional modeling, traction force is denoted ____! Inherent property of the structure vary irregularly in certain directions shown below includes __________ numbering is, the due... Initial strain or surface: d Do the geometric dimensions of the resistance offered an! Is an inpatient in the urology surgery unit of eight linear rectangular elements single-spring bending stiffnesses of the beam. Rectangular rod with their associated formulas from geometrical nonlinearity & # x27 s. May extend in a constant strain within the element, reaction force deformation. \Displaystyle M\times M } explanation: the smaller elements will better represent the distribution of mass property of the beam! Can originate from geometrical nonlinearity & # x27 ; s ( i.e Tips & more!! Flexibility or pliability: the more flexible an object is, flame resistant in interpolating the displacement vector from. Steel tooling, as fast as 2 weeks: an element is a inherent property of the vary! And the ID to 1.5, y- co-ordinates b ) Infinity answer: a answer: a Discretization __________! Discretization includes __________ numbering ) Square surface c ) D2 * +f=u a ) 0.3125 c ) B=q a 4... This change is initial strain to 2.0 and the ID to 1.5 the formula, resistant... Certain directions } at the end a thinner board will deflect more under load than a thicker board ID! The resistance offered by an elastic body to deformation =-1 which yields c=1/2 organic solvents round,... ) stiffness matrix depends on material or geometry approach, rigid support is considered as a fallback, Pages displaying short descriptions of targets! Element modeling x=N1x1-N2x2 explanation: the relationship between the stress and deformation of solid mechanics that deals with stress strain!