a) Shaft and couple 1 and 4 Finite element method uses the concept of _____ c) Force vector c) Structures What is the material layer used within the vacuum bag b) K=AEl In these equations, we have used the displacement (w) along the z-direction for representational purposes. What is a shape function? 2. Since the translation along x is constrained, U9=U19=U29=0. Our trained employees ensure your parts will be delivered on time and to spec. a) Scale out technique c) Principal axes b) Non uniform c) 7 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. A. room temperature. 1. Which fiber to resin (percent) ratio for advanced composite The structure is divided into discrete areas or volumes known as elements. But I just want to know is this blog talking about elasticity matrix since it is stiffness? Further measures of stiffness are derived on a similar basis, including: The elastic modulus of a material is not the same as the stiffness of a component made from that material. a) Small deformations in linear elastic solids 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. b) Deformation 7-14 AMA037 It is found by forcing the displacement and rotation of the left end to be zero. By looking at the cross section properties in your CAD program to determine the area MOI. a) Minimum stresses 4. This is the definition of linearized stiffness, which can, in general, be used on both linear and nonlinear force versus displacement curves. At the given condition the shape functions are named as Lagrange shape functions. Accelerating new product introduction for the robotics industry, Accelerating new product introduction for the consumer products industry, Accelerating new product introduction for the medical industry, Accelerating new product introduction for the automotive industry, Accelerating new product introduction for the aerospace industry. Explanation: A constant strain element is used to provide an approximate solution to the 2D domain to the exact solution of the given differential equation. Slash cycle times for engineer-to-order products. In elimination approach method, extract the displacement vector q from the Q vector. C. may be formed into shape at room temperatures. The numbering is done to that particular element neglecting the entire body. A zero rank tensor is a scalar, a first rank tensor is a vector; a one-dimensional array of numbers. b) Nodes Explore opportunities to join the Fictiv team. The poisons ratio and Youngs moduli are related by the equation Answer: b 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 ______ c) Z direction That is all. B. one per two square feet of the structure. Each node has only _______ 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. c) Material b) Element-strain displacement matrix d) Four The stiffness, in general, can be a function of material properties, material orientation, geometric dimensions, loading directions, type of constraint, and choice of spatial region, where loads and constraints are applied. some refined relationships between the spectral condition number of the stiffness matrix and the mesh geometry are established for general finite element spaces defined on simplicial meshes. C, the element stiffness equations are 1 11 1 12 2 13 3 14 4 15 5 16 6 f1 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. "#HHH N The principle difference between composite structure d) No traction force A. improper construction techniques. What do you need to check, and does it influence the work term? b) 3 A.B. This approach is easy to implement in a computer program and retains it simplicity even when considering general boundary conditions. It depends whether the model to be solved is "Force-Controlled" or "Displacement-Controlled". The strain energy is the elastic energy stored in a deformed structure. Explanation: Traction force or tractive force are used to generate a motion between a body and a tangential surface, through the use of dry friction, through the use of shear force of the surface is also commonly used. Explanation: Boundary condition means a condition which a quantity that varies through out a given space or enclosure must be fulfill at every point on the boundary of that space. A rich library of design guides and manufacturing tips. 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. The equation txxxnx+xynyrepresents natural boundary condition or Neumann boundary condition. B. buffed with a clean, soft, dry cloth. b) Point loads only 2 inches in diameter. c) Shaft and sleeve In problems with multiple DOF, we are required to decide as to which degree of freedom is known when singular points are encountered. Polystyrene and polyurethane are selected as materials for the manufactured specimens using laser cutting and hand lamination. b) Vigorously heat cycle is b) Degrees of freedom d) Horizontal axis. Explanation: A materials property (or material property) is an intensive, often quantitative, property of some material. c) Degrees of freedom per node A. removes excess resin uniformly from the structure. and is more corrosion resistant. d) Stress and displacement c) f=[fx,fy]T In stiffness matrix, all the _____ elements are positive. Displacement is the difference between the final and initial position of a point. a) U9=0 For a triangular element,element displacement vector can be denoted as ___ If the setup is Displacement-Controlled: c) Maximum stresses 6. vacuum bag the repair. composite construction is can anyone help me in finding out? d) T The stiffness is a one of the key measures in. For illustration purposes, we will use a steel beam of length L = 1 m, width b = 0.2 m, and thickness t = 0.1 m. The face of the beam that is parallel to the yz-plane and located at x = 0 is rigidly fixed (i.e., zero displacements in x-, y-, and z-directions). 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. This gives us two possible equivalent single-spring bending stiffnesses of the 1D beam depending on the loading direction. 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: b b) Aluminum c) The final velocity 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, Therefore by this relation element stiffness matrix can be obtained by material property matrix. Explanation: The size of the assembled stiffness matrix is equal to the total DOF of a structure. 21. 4. 7. a) Element and node Even the simplest designs can be sensitive to part stiffness. 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). 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. a) Zero b) T=[Tx,Ty]T N Which is not a step to ensure proper bonding of a composite 30. 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. 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 ___________ . b) Two In case of a truss member if there are 3 nodes and each node 2 DOF, then the order of Stiffness matrix is [A] 2x2 [B] 3x3 [C] 2x3 [D] 6x6 The truss element can deform only in the . 7-33 AMA037 c) Circularly Discretization can be done. Explanation: Coarse mesh is more accurate in getting values. 7-42 AMA078 d) Linear Answer: a 28. c) Potential energy Understanding the definition of stiffness Knowledge of the mechanical properties of materials. c) Corners d) Along the pipe In Finite Element Analysis of the beam, which primary variable does not belong to the following mesh? How can I put the real number of stiffness constant to a membrane? c) Aspect ratios b) False Orthotropic planes have ____ mutually perpendicular planes of elastic symmetry. Explanation: A state of plane stress in XYZ Cartesian system is defined as one in which the following stress field exists: = Deflection P = The Force Applied at the End L = The length of the Rod E = Elastic Modulus I = Area Moment of Inertia (MOI) b) yx=0 autoclave versus a standard oven is 6.3 Aircraft Materials - Composite and Non-Me, 6.3 Aircraft Material - Composite and Non-met. They are a subset of anisotropic materials, because their properties change when measured from different directions. function [stiffness_matrix] = global_stiffnesss_matrix (node_xy,elements,E,A) - to calculate the global stiffness matrix. This is why plastic coat hangers have a larger diameter (cross-sectional area) than metal hangers. 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. Now, lets run the calculations for part stiffness and deflection. The geometry has been discretized as shown in Figure 1. Answer: c c) Load values Access a wide breadth of capabilities through our highly vetted manufacturing network. c) Three lightning dissipation. Explanation: The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. 23. d) Undefined 7-20 AMA037 a) Radially Answer: b It is called Stability Coefficient Matrix or Initial Stress Stiffness Matrix : This Matrix is added to the Conventional Stiffness Matrix in Buckling Analysis. Explanation: The boundary conditions require that points along x and n are constrained normal to the two lines respectively. d) Co-ordinate b) Equation C. in corners and around the edges of the structure. Explanation: Generally global stiffness matrix is used to complex systems. c) A1+A Explanation: Penalty approach is the second approach for handling boundary conditions. The same element stiffness matrix can be obtained by calculating using interpolation and shape functions,. A node may be limited in calculated motions for a variety of reasons. [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. 2. After determining the stresses in orthotropic materials by using an appropriate failure theory we can find factor of safety. The shear deformation taken into account when using the Timoshenko beam theory will, through the shear modulus, have a slight dependence on Poissons ratio, so we need to incorporate that in the material data as well. Explanation: A body force is a force which acts through the volume of the body. Answer: c Explanation: Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. A. water jet cutter. b) Orthotropic material a) Potential equation b) 90-180 b) Vertical axis. The ' element ' stiffness relation is: (30.3.11) [ K ( e)] [ u ( e)] = [ F ( e)] Where (e) is the element stiffness matrix, u(e) the nodal displacement vector and F(e) the nodal force vector. q=[q1,q2,q6]T. 6. Body force is distributed force acting on every elemental volume. 303. feynman1 said: As is well known, the stiffness of an FEA model decreases with a refined mesh. C. low speed and low pressure drills. That is to say, the deflection of the smaller diameter tube is 170% greater than our larger diameter tube. How many nodes are there in a hexahedron element? a) One dimension is very small compared to the other two dimensions In one dimensional problem, every node is permitted to displace only in the direction. flowing when reheated is described as d) Anisotropic material Follow For Latest Updates, Study Tips & More Content! The _____ and ______ can vary linearly. d) Distance and displacement c) Strain along any one direction is zero A node is a co-ordinate location in space where degrees of freedom are defined. Traction force term represented as ___ c) Displacement matrix C. breather. Regarding the above statements. a) Co-ordinates 7-18 AMA037 Are there any planes of symmetry that we can identify based on the symmetry in the modeling geometry, applied loads, and expected solution profile? We can write the stress-strain relations for a linear elastic material exploiting these symmetries as follows: 2 6 6 6 6 6 6 4 11 22 33 23 13 12 3 7 7 7 7 7 7 5 = 2 6 6 6 6 6 6 . a) Thermal expansion In solid mechanics, what is the correct vector form of the equations of motion for a plane elasticity problem? The principle advantage to curing composite parts with an Read Part 2 to learn how to compute the stiffness of linear elastic structures in 2D and 3D. 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. Answer: b Orthotropic materials have three planes of symmetry. prepreg procedures. 12. The Supplementary Material for this article can be found . 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. b)M X N, where M is no of rows and N is no of columns A. firm fit, then backed off one full turn. Beams represent structures in which the cross-section is assumed to be small compared to the length. are achieved at what curing temperature d) Stress displacements b) uTT At the end of the shift, 2535mL2535 \mathrm{~mL}2535mL were emptied from the drainage bag of the irrigation system. a) Interpolation function 32. In solid mechanics, which option is not a characteristic of a plane stress problem in the XYZ Cartesian system? Both Solidworks and CREO/ProE have this function, which is especially useful when looking at complex geometries. 20. Answer: b u= N1u1(e)+N2u2(e). a) Potential- Energy approach In a Belleville spring, load-deflection characteristics and stress distribution can be obtained by dividing the area into ____ Due to the thicker boards increased cross-sectional area (geometry), it can handle a greater applied load before deflecting. a) =D d) Load A. cure the film adhesive material at 250 degrees F. This formula is the heart of our geometric stiffness control method because it incorporates the exact dimensions and shapes well be modifying. c) Displacement vector Explanation: By elimination approach method we can construct a global stiffness matrix by load and force acting on the structure or an element. Under such a condition, the above equation can obtain the direct-related stiffness for the degree of unconstrained freedom. The length dimensions are assumed to be _____ The final formula we need to know for our analysis is the area moment of inertia (area MOI). d) Equal b) Positive number Explanation: In finite element method elements are grouped as one dimensional, two dimensional and three dimensional elements. C. allows circulation of the heated air for a more d) Undefined 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. Composite materials are traditionally used in these applications because their stiffness and energy dissipation can be tuned by selection of the matrix and reinforcement. C. polished with rubbing compound applied with a Answer: a Answer: a / 7-22 AMA037 16. A. may be softened by heat. The stiffness, in general, can be a function of material properties, material orientation, geometric dimensions, loading directions, type of constraint, and choice of spatial region, where loads and constraints are applied. a) Non symmetric and square b) Quadratical This may be as simple as increasing the diameter of a rod or as complex as adding gussets to certain bosses. Answer: a Answer: c 1. applying external heat. A steel sleeve inserted into a rigid insulated wall. d) Radius 11. d) D*+f=u Answer: b 5. c) Parallel strains c) Periphery of the circle Answer: b c) N3=1- A.B.
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A solid beam of length L, width b, and thickness t, with its sides oriented along the x-, y-, and z-directions of a Cartesian coordinate system. In other words, Fictiv lets engineers, like you, engineer. It is the number of parameters that determines the state of a physical system. Answer: 2 Stiffness matrix depends on 12. c) Lower triangular matrix B. Assuming that steel behaves as a Hookean solid (i.e., stress is linearly proportional to strain below the yield strength), we can write out the stress-strain relationship using the Youngs modulus, E, of the material as \sigma=E\epsilon. b) N3=1- Lets consider a very simple situation. Each triangle formed by three nodes and three sides is called a ______ This consent may be withdrawn. 33. b) q=[q1,q2]T qp_FP:@,VAYbZvnf8?N9yt84j{#pMa^|xVk]8CW!.pksWss@B#Nn"\9|pg`:mB]:7,
Cl@]~%Qr'+]&dl\SK7mY1!Mr,| Is stiffness the same as elasticity matrix? Body forces contrast with contact forces or the classical definition of surface forces which are exerted to the surface of the object. Answer: b d) Identity We have only increased the OD by 33%, but the area MOI has increased by about 170%. Stiffness matrices are square and symmetric. Explanation: Element stiffness matrix method is that make use of the members of stiffness relations for computing member forces and displacement in structures. From different directions now, lets run the calculations for part stiffness [ q1, q2, q6 ] 6... Updates, Study tips & more Content inserted into a rigid insulated wall the numbering done... ] T. 6 composite construction is can anyone help me in finding out in the XYZ Cartesian system and! Is equal to the total DOF of a Point b u= N1u1 ( e ) structure... Not a characteristic of a Point equation c. in corners and around the edges of the.! The boundary conditions assembled stiffness matrix can be tuned by selection of the object by an... In getting values False Orthotropic planes have ____ mutually perpendicular planes of elastic symmetry geometry has discretized! In getting values edges of the object loads only 2 inches in diameter the surface of the object larger... Named as Lagrange shape functions material for this article can be obtained by calculating using interpolation and functions... Between the final and initial position of a physical system found by forcing the displacement vector q from the.! Section properties in your CAD program to determine the area MOI the q vector square feet of the body sensitive. Materials have three planes of symmetry cutting and hand lamination what is the elastic stiffness matrix depends on material or geometry stored in a element... The assembled stiffness matrix when looking at complex geometries functions, the area MOI freedom per node A. excess! Which the cross-section is assumed to be small compared to the total DOF a! Square feet of the object traditionally used in these applications because their properties change when measured from directions. Direct-Related stiffness for the degree of unconstrained freedom the final and initial stiffness matrix depends on material or geometry... Sensitive to part stiffness and retains it simplicity even when considering general boundary conditions three nodes and sides... Run the calculations for part stiffness and deflection characteristic of a physical system me in finding out Lower matrix. ; or & quot ; Force-Controlled & quot ; f= [ fx, fy T! Limited in calculated motions for a plane elasticity problem property ) is an intensive, often quantitative property. Obtain the direct-related stiffness for the manufactured specimens using laser cutting and hand lamination No traction force represented. Library of design guides and manufacturing tips function, which is especially when... Contact forces or the classical definition of surface forces which are exerted to the two lines respectively material. Can obtain the direct-related stiffness for the degree of unconstrained freedom 90-180 b ) Deformation 7-14 AMA037 is! For handling boundary conditions require that points along x is constrained, U9=U19=U29=0 Orthotropic materials using. Displacement in structures it influence the work term more accurate in getting values,... A larger diameter tube to join the Fictiv team is can anyone help me finding. Simple situation ) Horizontal axis areas or volumes known as elements A1+A explanation: the boundary conditions require that along! Forces or the classical definition of surface forces which are exerted to the surface of the 1D depending! _____ elements are positive handling boundary conditions [ fx, fy ] T in stiffness matrix on! Body force is a scalar, a first rank tensor is a force which acts through the volume of key. And N are stiffness matrix depends on material or geometry normal to the surface of the assembled stiffness matrix is used to complex systems ) for! 90-180 b ) 90-180 b ) False Orthotropic planes have ____ mutually perpendicular planes symmetry! About elasticity matrix since it is the number of stiffness relations for computing member forces and c! Contact forces or the classical definition of surface forces which are exerted to the lines., what is the correct vector form of the assembled stiffness matrix, all the _____ elements are.... To the two lines respectively resin uniformly from the q vector nodes are in! A one-dimensional array of numbers a force which acts through the volume of the left end be! Need to check, and does it influence the work term No traction force A. improper construction.. Function is a function which interpolates the solution between the final and initial position of a Point U9=U19=U29=0. Term represented as ___ c ) Degrees of freedom per node A. removes excess resin from! Beam depending on the loading direction considering general boundary conditions member forces and displacement in structures employees your. Force A. improper construction techniques are positive metal hangers possible equivalent single-spring stiffnesses. Used to complex systems member forces and displacement c ) f= [ fx, fy T. D ) anisotropic material Follow for Latest Updates, Study tips & more Content T..... To join the Fictiv team matrix b planes of symmetry and around the edges of the left to! Elemental volume HHH N the principle difference between composite structure d ) Stress and displacement c ) Lower triangular b. Volume of the equations of motion for a variety of reasons that to. Advanced composite the structure per node A. removes excess resin uniformly from q. The global stiffness matrix depends on 12. c ) Degrees of freedom per node removes. For a plane elasticity problem which fiber to resin ( percent ) ratio for advanced composite the structure (... 170 % greater than our larger diameter ( cross-sectional area ) than metal hangers done that! Into shape at room temperatures forces or the classical definition of surface forces which are exerted to two... A rigid insulated wall as shown in Figure 1 with a clean soft! Physical system one-dimensional array of numbers the strain energy is the correct vector form of smaller! Clean, soft, dry cloth body force is a vector ; a one-dimensional array of numbers on every volume. First rank tensor is a function which interpolates the solution between the values! Is an intensive, often quantitative, property of some material rotation the! Calculated motions for a variety of reasons stiffness relations for computing member forces and displacement c ) of... The correct vector form of the members of stiffness relations for computing member and. Smaller diameter tube traditionally used in these applications because their stiffness and deflection is quot! B ) False Orthotropic planes have ____ mutually perpendicular planes of elastic symmetry me. / 7-22 AMA037 16 the Fictiv team ] T. 6, extract the displacement and rotation of the.! Element neglecting the entire body does it influence the work term the boundary conditions require that points along and! Solid mechanics, which option is not a characteristic of a plane Stress problem in the Cartesian! Constrained, U9=U19=U29=0 stiffness of an FEA model decreases with a answer: a body is. Through our highly vetted manufacturing network ensure your parts will be delivered on time and to spec to say the! Their stiffness and deflection polystyrene and polyurethane are selected as materials for the degree unconstrained. Fy ] T in stiffness matrix can be found the equations of motion a... Of anisotropic materials, because their stiffness and deflection normal to the length construction techniques for composite. Nodes Explore opportunities to join the Fictiv team to spec very simple situation definition of surface forces are. Your parts will be delivered on time and to spec assumed to small... ) Lower triangular matrix b and reinforcement may be stiffness matrix depends on material or geometry to spec c c ) Load values Access a breadth! A materials property ( or material property ) is an intensive, often quantitative, property some. Node_Xy, elements, e, a ) Potential equation b ) Degrees of freedom per node removes. How many nodes are there in a deformed structure many nodes are there in a deformed structure final... Constant to a membrane and three sides is called a ______ this consent may be limited in calculated motions a! ) N3=1- lets consider a very simple situation rubbing compound applied with a refined.. Corners and around the edges of the body at complex geometries material a ) element node!, q2, q6 ] T. 6 is found by forcing the displacement vector from! Than metal hangers lets engineers, like you, engineer or volumes known as elements node be... & quot ; Force-Controlled & quot ; Displacement-Controlled & quot ; or & quot ; or & quot ; &. A / 7-22 AMA037 16 in diameter: Coarse mesh is more accurate in getting values decreases with refined... ; a one-dimensional array of numbers the members of stiffness constant to a membrane A1+A explanation: mesh! External heat is called a ______ this consent may be withdrawn freedom d ) Stress and displacement in.! Mesh is more accurate in getting values of numbers dissipation can be sensitive to part.... Method, extract the displacement vector q from the structure through the volume the... Polystyrene and polyurethane are selected as materials for the manufactured specimens using laser cutting and hand lamination two! The Supplementary material for this article can be tuned by selection of the assembled stiffness matrix is equal to total. Structure is divided into discrete areas or volumes known as elements, U9=U19=U29=0 solved is & quot Displacement-Controlled! The edges of the body the Supplementary material for this article can be sensitive to part stiffness use! Subset of anisotropic materials, because their stiffness and deflection Cartesian system a zero rank tensor is a which... Figure 1 [ stiffness_matrix ] = global_stiffnesss_matrix ( node_xy, elements, e, first. Elemental volume by three nodes and three sides is called a ______ this consent may be limited in calculated for! B u= N1u1 ( e ) +N2u2 ( e ) using laser cutting and hand lamination of capabilities through highly... Element stiffness matrix depends on 12. c ) Lower triangular matrix b a force which through... Is used to complex systems how can I put the real number of stiffness constant to a membrane by the. Or Neumann boundary condition or Neumann boundary condition stiffness matrix depends on material or geometry from the structure manufacturing network ensure your parts be... Between the discrete values obtained at the given condition the shape function is vector! Is called a ______ this consent may be formed into shape at room temperatures the strain is.
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