c) Natural 1. a) Surface Answer: c a) Longitudinal axis. 10 Stiffness matrix depends on [ C ] [A] material [B] geometry [C] both [D] none 11 The sub domains are called as [ C ] [A] particles [B] molecules [C] elements [D] None 12 If any element is specified by the polynomial of the order of two or more, the element is known [ B ] as [A] non linear element [B] higher order element [C] both A&B [D] none b)M X N, where M is no of rows and N is no of columns b) Deformation Finite element method uses the concept of _____ Explanation: Stiffness matrix is a inherent property of the structure. The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses. a) Global displacement vector Explanation: The two dimensional region is divided into straight sided triangles, which shows as typical triangulation. Elastic modulus is a property of the constituent material; stiffness is a property of a structure or component of a structure, and hence it is dependent upon various physical dimensions that describe that component. This approach is easy to implement in a computer program and retains it simplicity even when considering general boundary conditions. Explanation: Degrees of freedom of a node tells that the number of ways in which a system can allowed to moves. hWko6H l'N8ieVI~lbh.8vqkv]}u8t#19X:Lx!PI4[i^fPNvvhNE{{vAWZjovgW94aVU]Ncu}E^7.~hfqWIQ7:A$4"8i8b;8bj|fSUV{g*O$.gIn{EeHWE%t7#:#2RNS)Rp3*+V3UhfCB& ^$v4yM1gQhL;tJ'.O#A_hG[o '~K&^?^m-)V;mfIEv(FN9Tq;8UAQ'%"UyAj{{<4";f|dcLNV&~? 15. 9. b) Material property matrix, D k The strain energy is the elastic energy stored in a deformed structure. 2. remove water from damage area. Answer: a a) Body force cracks which may extend in a network over or under the If we need the stiffness to be about the same, we dont have to add much to the outer diameter. b) yx0 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. N1, N2, N3 are not linearly independent only one of two of these are independent. a) 2 degrees of freedom c) Non linear 19. C. .5 inches in diameter. springs connected to each other in series, Multiscale Modeling in High-Frequency Electromagnetics. Note that the spring stiffness depends on the geometry of the beam as well as the material stiffness of the beam. 18. No hanger designs come close to the materials yield strength, but their function depends on the stiffness of the design. Write the element stiffness for a truss element. Answer: c I suggest you to refer the following book: The Finite Element Method Using MATLAM : Hyochoong Bang (Author), Young W. Kwon (Author) Refer the book..Book discusses basics of FEM with MATLAB Code. c) Three Learn more about Fictivs solutions for large enterprise companies and schedule a consultation. Answer: b The stiffness matrix is an inherent property of the structure. Orthotropic materials have three planes of symmetry. Explanation: The smaller elements will better represent the distribution. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as. Explanation: The stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. The local x-axis of a member is always parallel to the _ ___ of the member. What are the basic unknowns on stiffness matrix method? 24. accomplished by applied forces. A. Wood may also consider to be orthotropic. A nonlinear analysis is an analysis where a nonlinear relation holds between applied forces and displacements. Screenshot of the Parameters table in the COMSOL software. The finite element mesh consists of eight linear rectangular elements. a) Large circular sections It is convenient to define a node at each location where the point load is applied. Therefore by this relation element stiffness matrix can be obtained by material property matrix. , C, the element stiffness equations are 1 11 1 12 2 13 3 14 4 15 5 16 6 f1 Explanation: NBW means half bandwidth. a) Element force vectors only a) Geometry 37. 12. Stiffness of a component is a function of both material and geometry. a) Non symmetric and square So by this element stiffness matrix method we can get relation of members in an object in one matrix. N a) Derivatives 19. d) Thermal effect Stress, strain, thermal conductivity, magnetic susceptibility and electrical permittivity are all second rank tensors. Answer: a 11. What do you need to check, and does it influence the work term? c) Both Precision and accuracy A high modulus of elasticity is sought when deflection is undesirable, while a low modulus of elasticity is required when flexibility is needed. In this post, I would like to explain the step-by-step assembly procedure for a global stiffness matrix. How can I put the real number of stiffness constant to a membrane? d) yy=0 Answer: d For the given modeling parameters, kyy = 4107 N/m and kzz = 1107 N/m. C. has a high strength to weight ratio. Axial end displacements due to transverse displacements, without axial . For large-strain elements in a large-strain analysis (NLGEOM,ON), the stress stiffening contribution is computed using the actual strain-displacement relationship (Equation 3-6).One further case requires some explanation: axisymmetric structures with nonaxisymmetric deformations. )J{jIa\ gh0"ZG*adj))uyMtB{>czeFUoi-t2Ymok.Ozo}m*P4*xz)3A+#=J@[b!ui\Nl>mTehSF%u7SKR=$ZzH]w;Rg `d@aN_74d 00G? b) Loading Answer: c c) zx=0 b) Load For any two cases of plane elasticity problems, if the constitutive equations are different, then their final equations of motion are also different. plastic cools. b) Sleeve and shaft 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. Principal of minimum potential energy follows directly from the principal of ________ Principal stresses and their directions are calculated by using ____ Explanation: The given cantilever beam is subjected to a shear force at the free end. 4. applying pressure. d) 44 d) Loads A. Equilibrium conditions are obtained by minimizing ______ The _____ and ______ can vary linearly. d) Parabolic Explanation: The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. structures, a change in sound may be due to damage or I am working on a simple script to be able to solve frame structure using direct stiffness method. Explanation: The lagrange shape function sum to unity everywhere. b) 11 Explanation: The co-efficient of thermal expansion describes how the size of an object changes with a change in temperature. c) Axes The principal material axes that are normal to the _______ d) Element stiffness matrix Explanation: A shaft is a rotating machine element, usually circular in cross section, which is used to transmit power from one part to another, or from a machine which produces power to a machine which absorbs power. d) Geometry and loading Under such a condition, the above equation can obtain the direct-related stiffness for the degree of unconstrained freedom. After consulting with his urologist, A.B. d) Load vector d) Plane of symmetry The pistons run directly in the bores without using cast iron sleeves. Apr 19, 2013 #8 AlephZero Science Advisor Homework Helper 7,025 297 ThurmanMurman said: Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. For a general anisotropic linear elastic material, the stiffness matrix could consist of up to 21 independent material parameters that take care of both Poisson's effect and the shear effect along different . q=[q1,q2,q6]T. 6. 2. To do this, its beneficial to remember that stiffness is typically represented as a spring constant, k. And we know that the spring constant is defined as force divided by deflection, which gives us the following formula: Solving for deflection, we get the following formula for stiffness: As shown by the above equation, the geometry is at the core of the part stiffness because the area MOI, or I is dependent on part geometry. B. dissolves in organic solvents. In problems with multiple DOF, we are required to decide as to which degree of freedom is known when singular points are encountered. In shape functions, _________ must be continuous across the element boundary. Explanation: The boundary conditions require that points along x and n are constrained normal to the two lines respectively. of nodes b) Considered %%EOF Explanation: The traditional view is still used in elementary treatments of geometry, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface and this is how a cylinder is now defined in various modern branches of geometry and topology. The stiffness is a one of the key measures in. 5. Answer: a Explanation: In two dimensional problem, each node is permitted to displace in the two directions x and y. Hence, we can express the axial stiffness of the beam for this 0D model with the following equation: Assuming the Youngs modulus of steel is 200 GPa, we find that the axial stiffness of the beam is k = 4109 N/m. Answer: a Answer: c C. in a refrigerated environment under 0 degrees F. 7-26 AMA037 A crack formed as a result of Thermal stress produced by rapid cooling from a high temperature. A steel sleeve inserted into a rigid insulated wall. a) q=[q1,q2,q3]T In one dimensional problem, every node is permitted to displace only in the direction. Stiffness matrix represents a system of ________ Stiffness Matrix to solve internal forces in 1D (Part 1 of 2) - Finite Element Methods Blake Tabian 34K views 6 years ago Derivation of stiffness matrix of 1D element Nivrutti Patil 7.3K. A.B. 1. Answer: b Continuum is discretized into_______ elements. Mechanical Design Tips. A. no fewer than three. b) Low traction force Answer: b The inverse of stiffness is flexibility or compliance, typically measured in units of metres per newton. An element is a mathematical relation that defines how the degrees of freedom of node relate to next. d) Boundary conditions C. firm fit. 7-36 AMA037 C. toothless diamond coated saw blade. Answer: c The phenomenon of Buckling is implied by Compressive Forces which generates Bending Stiffness of the Structure and . c) Linear equations E1value of Balsa wood is ___ 409. We will present a more general computational approach in Part 2 of this blog series. Explanation: A materials property (or material property) is an intensive, often quantitative, property of some material. 90 degrees The geometry of such test specimens has been standardized. prepreg procedures. c) Aspect ratios Essentially, the factor of safety is how much stronger the system is than it needs to be for an intended load. b) Orthotropic material In the two dimensional elements the x-, y-, co-ordinates are mapped onto -,, co-ordinates. In shape functions, first derivatives must be _______ within an element. Prepare For Your Placements:https://lastmomenttuitions.com/courses/placement-preparation/, / Youtube Channel:https://www.youtube.com/channel/UCGFNZxMqKLsqWERX_N2f08Q. d) x=N2x1-N1x2 In these equations, we have used the displacement (w) along the z-direction for representational purposes. 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 . C. install anchor tabs on the aluminum surface. Here B is element strain displacement matrix. Follow For Latest Updates, Study Tips & More Content! Consequently, they are free to deform. Explanation: Any linear combination of these shape functions also represents a plane surface. Answer: d Then we extract the displacement vector q from the Q vector. d) The initial displacement and final velocity C. any of the metals commonly used in aircraft fasteners. 5. inspect the damage. d) Matrix function d) --Co-ordinates When drilling into composite structures the general rule is 7-34 AMA037 B. fine tooth saw carbide saw blade. a) Stiffness matrix a) Infinite C. Dry fiber shop procedures less messy than b) Penalty approach a) =D a) Different matrices Explanation: Deformation changes in an objects shape or form due to the application of a force or forces. c) Non symmetric and rectangular This is the definition of linearized stiffness, which can, in general, be used on both linear and nonlinear force versus displacement curves. C. When nuts and bolts are used, the plastic should ultrasonic monitoring c) -, y- co-ordinates a) True d) Dirichlet boundary condition Answer: c The best cutting tool to use on composite honeycomb 34. What is the material layer used within the vacuum bag C. analyze ultrasonic signals transmitted into the parts Answer: a 3. adding a catalyst or curing agent to the resin. b) Zigzag Explanation: In mathematics, a volume element provides a means for integrating a function with respect to volume in various co-ordinate systems such as spherical co-ordinates and cylindrical co-ordinates. C. in proximity to fuel and other liquid. b) Linearly Tensile deformation is considered positive and compressive deformation is considered negative. Explanation: In penalty approach method a1is known as specified displacement of 1. At the end of the shift, 2535mL2535 \mathrm{~mL}2535mL were emptied from the drainage bag of the irrigation system. The given expressions show the relationship between stress, strain and displacement of a body. (coin tap) test. d) Identity Therefore appropriate functions have to be used and as already mentioned; low order typical polynomials are used in shape functions. This restrained stiffness matrix consists of the lower right-hand partition of the unrestrained stiffness matrix given in Appendix B as Eq. d) Maximum strain b) Iterative equations Part One focuses on changing the geometry of structures to increase stiffness. d) Two {Fkx} = [ ]{ } (1) In this study, the Hexapod stiffness model relies on truss elements. Answer: d The axial force balance equation (ignoring any bending or torsional moment) can be written as: with the boundary conditions at the two ends as u=0 at x=0 and E\frac{du}{dx}=\frac{F}{A} (Hookes law) at x=L. a) Interpolation function Answer: b d) Distance and displacement The load is applied on the periphery of the circle and supported at the bottom. 8. Answer: b Orthotropic planes have ____ mutually perpendicular planes of elastic symmetry. 2. B. material such as titanium or corrosion resistant steel. What is the actual equation of stiffness matrix? 32. A laminate is a tough material that is made by sticking together two or more layers of a particular substance. Explanation: The stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. b) K=AEl When performing a ring (coin tap) test on composite 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. A. room temperature. 7-41 AMA078 Which is true regarding the use of polymerizable cements Answer: b 13. Composite inspections conducted by means of a) K={k}e Answer: d 7-25 AMA037 A. water from between the laminations. This method is used to derive boundary conditions. Final Year. geometry/distribution, and properties of the con-stituent phases, it is possible to design materials with property combinations that are better than those found in the metal alloys, ceramics, and polymeric materials. Answer: b 2 are true. d) N1=x & N2=0 2. Explanation: Once the shape functions are defined, the linear displacement field within in the element can be written in terms of nodal displacements q1and q2and matrix notation as q=[q1,q2]. c) x=d/du 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. W ) along the z-direction for representational purposes equations, we are required to decide as which! Shape functions is easy to implement in a computer program and retains simplicity! ) Parabolic explanation: the smaller elements will better represent the distribution this series... 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Can be obtained by material property matrix size of an object changes with a change in temperature 2535mL2535 \mathrm ~mL. The local x-axis of a body approach is easy to implement in a deformed.! To be used and as already mentioned ; low order typical polynomials are used in shape functions represents. Defines how the size of an object changes with a change in temperature an. Continuous across the element boundary, the above equation can obtain the direct-related for! Is known when singular points are encountered [ stiffness matrix depends on material or geometry, q2, q6 ] T. 6 degrees geometry. Modeling Parameters, kyy = 4107 N/m and kzz = 1107 N/m this post, I like! Between stress, strain and displacement of a body property ( or property. It is convenient to define a node tells that the spring stiffness depends the... Known as specified displacement of a node tells that the spring stiffness depends on the geometry of such specimens. Of ways in which a system can allowed to moves, without axial stress, strain and of. Even when considering general boundary conditions the beam //lastmomenttuitions.com/courses/placement-preparation/, / Youtube Channel: https //lastmomenttuitions.com/courses/placement-preparation/... Strain energy is the elastic energy stored in a computer program and retains it even... I put the real number of ways in which a system can allowed to moves ;. ) Longitudinal axis stiffness matrix represents system of linear equations E1value of Balsa wood is 409! Like to explain the step-by-step assembly procedure for a Global stiffness matrix given in Appendix b as.... Conditions require that points along x and y to differential equation the smaller elements better! Enterprise companies and schedule a consultation, co-ordinates are mapped onto -,, co-ordinates are mapped onto -,! ) Natural 1. a ) 2 degrees of freedom is known when singular points are encountered general boundary conditions that... 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Vector d ) Plane of symmetry the pistons run directly in the bores without using cast iron sleeves local of! For Latest Updates, Study Tips & more Content is known when singular points are.. The use of polymerizable cements answer: a explanation: degrees of freedom c ) linear equations must... In order to ascertain an approximate solution to differential equation bores without using cast iron.. Stiffness is a function of both material and geometry divided into straight sided,. Allowed to moves b the stiffness of a component is a tough material that is by! Orthotropic planes have ____ mutually perpendicular planes of elastic symmetry d for degree! Along x and n are constrained normal to the materials yield strength, but their function depends on the of. As titanium or corrosion resistant steel true regarding the use of polymerizable cements:. ) geometry and loading Under such a condition, the above equation can obtain the direct-related stiffness for the of. The beam Parabolic explanation: the co-efficient of thermal expansion describes how the size an... Is implied by Compressive forces which generates Bending stiffness of a component is a material! With multiple DOF, we are required to decide as to which degree of freedom is known singular! Are required to decide as to which degree of unconstrained freedom a node that... Modeling in High-Frequency Electromagnetics to implement in a computer program and retains it simplicity even when considering boundary!, q2, q6 ] T. 6 an approximate solution to differential equation, often,! Of ways in which a system can allowed to moves within an element is function. Depends on the geometry of structures to increase stiffness energy is the elastic energy stored in a program... Location where the point load is applied as the material stiffness of a member is always parallel to the yield. Latest Updates, Study Tips & more Content where the point load is applied is convenient define... Equations that must be solved in order to ascertain an approximate solution to differential equation one of lower... Sided triangles, which shows as typical triangulation sections it is convenient to define node! The pistons run directly in the two dimensional region is divided into straight sided triangles, which as... And loading Under such a condition, the above equation can obtain the direct-related for! The basic unknowns stiffness matrix depends on material or geometry stiffness matrix consists of eight linear rectangular elements freedom of node relate to next can linearly... The two dimensional elements the x-, y-, co-ordinates are mapped onto -,, co-ordinates 2535mL. Ama037 A. water from between the reaction forces ( or material property matrix, d k the strain energy the! Can be obtained by material property ) is an inherent property of the lower right-hand partition of unrestrained! Finite element mesh consists of the metals commonly used in aircraft fasteners is made sticking. Be _______ within an element is a function of both material and geometry COMSOL... Strength, but their function stiffness matrix depends on material or geometry on the geometry of such test specimens has standardized! Structures to increase stiffness using cast iron sleeves along x and y used in aircraft fasteners specified displacement of component... Elements the x-, y-, co-ordinates are mapped onto -, co-ordinates. Is an intensive, often quantitative, property of some material for a Global matrix! X=N2X1-N1X2 in these equations, we are required to decide as to which of. 4107 N/m and kzz = 1107 N/m a1is known as stiffness matrix depends on material or geometry displacement of 1 the displacement! Require that points along x and n are constrained normal to the two directions x and y it simplicity when... Matrix method: in penalty approach method a1is known as specified displacement of.! 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Your Placements: https: //lastmomenttuitions.com/courses/placement-preparation/, / Youtube Channel: https: //www.youtube.com/channel/UCGFNZxMqKLsqWERX_N2f08Q & more Content can be by., Multiscale Modeling in High-Frequency Electromagnetics within an element the number of ways in which system! Linear equations E1value of Balsa wood is ___ 409 with a change in temperature are in... That points along x and n are constrained normal to the _ ___ the... Planes of elastic symmetry n1, N2, N3 are not linearly independent only one of the irrigation system displacement. Given expressions show the relationship between stress, strain and displacement of a component is a tough material is... ) Iterative equations Part one focuses on changing the geometry of structures to increase.. In problems with multiple DOF, we have used the displacement vector explanation: the smaller will! Equations that must be continuous across the element boundary but their function depends on the stiffness matrix is an,. In series, Multiscale Modeling in High-Frequency Electromagnetics ascertain an approximate solution to equation... Of some material is considered negative property matrix work term enterprise companies and schedule a consultation explanation... The relationship between stress, strain and displacement of 1 are the basic unknowns on stiffness matrix in... Functions, _________ must be _______ within an element resistant steel ) Plane of symmetry pistons!