7-14 AMA037 Explanation: The two dimensional region is divided into straight sided triangles, which shows as typical triangulation. d) 2- direction and 4- direction Hi Sreenivas, Geometric Stiffness Matrix is often used in Buckling. Hopefully, this conveys the message that seemingly small increases in part diameter or height will greatly increase the part stiffness. Then reduced stiffness matrix can be obtained by eliminating no of rows and columns of a global stiffness matrix of an element. d) D*+f=u c) Adjoining matrix. The mathematical expression for the stiffness of the connection element is (1) To account for the effect of initial residue stresses, which is trapped in hot-rolled members during the cooling processes, a simplified approach from Reference 4 is used. c) Linear equations f=[fx,fy]T. 8. That is all. The gussets are added to increase the part stiffness and strength, but how do we calculate this without extensive hand calculations? Explanation: The process of dividing a body into equivalent number of finite elements associated with nodes is called discretization. Global nodes corresponds to _______ Answer: 2 Stiffness matrix depends on 12. B. anodize the aluminum surface. b) Orthotropic a) Shaft and couple a) High traction force 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 :. 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. A. high strength aluminum-lithium alloy. 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. Explanation: Degrees of freedom of a node tells that the number of ways in which a system can allowed to moves. Finite element method uses the concept of _____ a) Linear Explanation: Global load vector is assembling of all local load variables. Explanation: Penalty approach is one of the method to derive boundary conditions of an element or a structure. C. .5 inches in diameter. (The element stiffness relation is important because it can be used as a building block for more complex systems. c) Co-ordinates Therefore appropriate functions have to be used and as already mentioned; low order typical polynomials are used in shape functions. around edges or under fairings. C. a 60 percent matrix to 40 percent fiber ratio., 7-2 AMA037 Composite fabric material is considered to be . b) Two structures, a change in sound may be due to damage or A high modulus of elasticity is sought when deflection is undesirable, while a low modulus of elasticity is required when flexibility is needed. a) X direction Which of the following is true for the stiffness matrix (K)? b) Force matrix Answer: b {\displaystyle N/m} A good practice is to choose corner angle in the range of 30-120. Answer: b a) Surfaces Screenshot of the Parameters table in the COMSOL software. d) No. c) Identity matrix A material's stiffness indicates its ability to return to its original shape or form after an applied load is removed. Nonlinear analysis. Explanation: The best elements are those that approach an equilateral triangular configuration. d) Program SOLVING Explanation: Generally global stiffness matrix is used to complex systems. Again, this is very close to our 170% difference in the spreadsheet calculations. The overall reaction in the lead storage battery is Pb(s)+PbO2(s)+2H+(aq)+2HSO4(aq)2PbSO4(s)+2H2O(l)\mathrm { Pb } ( s ) + \mathrm { PbO } _ { 2 } ( s ) + 2 \mathrm { H } ^ { + } ( a q ) + 2 \mathrm { HSO } _ { 4 } ^ { - } ( a q ) \longrightarrow 2 \mathrm { PbSO } _ { 4 } ( s ) + 2 \mathrm { H } _ { 2 } \mathrm { O } ( l )Pb(s)+PbO2(s)+2H+(aq)+2HSO4(aq)2PbSO4(s)+2H2O(l) Based on your previous answers, why does it seem that batteries fail more often on cold days than on warm days? a) Stiffness matrix b) Element-strain displacement matrix The other end is supported by roller and hinge support. c) Elimination approach b) Normal strains a) Global displacement vector c) uT a) K=Al 4. Each triangle formed by three nodes and three sides is called a ______ b) Vigorously damp cloth. Explanation: A unidirectional (UD) fabric is one in which the majority of fibers run in one direction only. Study with Quizlet and memorize flashcards containing terms like 7-1 AMA037 The strength and stiffness of a properly constructed composite buildup depends primarily on A. the orientation of the plies to the load direction. b) Equation a) x-, y- co-ordinates Material stiffness is a measure of how much of a load it takes to cause elastic deformation in the material and is numerically represented by Youngs modulus (aka the modulus of elasticity). Answer: a So your stiffness matrix will be 8x8. 30. Explanation: By elimination approach method we can construct a global stiffness matrix by load and force acting on the structure or an element. d) Eliminated c) Aspect ratios 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). Explanation: A degrees of freedom may be defined as, the number of parameters of system that may vary independently. Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. B. allows curing in higher temperatures and pressures. Explanation: Strain energy is defined as the energy stored in the body due to deformation. Answer: d APDL Math is a tool for users to do two things: 1) get access to view, export or modify matrices and vectors created by the solver, and 2) to control import or modify matrices and vectors then solve them. 1 inch in diameter. Thus, xx0, yy0, zz0, xy0, where as yz=0 and zx=0. The determinant of an element stiffness matrix is always One zero depends on size of [K] Two Show Answer 2. If a circular pipe under internal or external pressure, by symmetry all the points move radially. composite fasteners having an order of, The determinant of an element stiffness matrix is always. a) Co-ordinates View Answer 3. c)Mb Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. b) Symmetric cracks which may extend in a network over or under the a) 0.125*106psi d) Nodes 35. The other end is supported by roller and hinge support. 25. Tight tolerances and finishing capabilities, as fast as 2 days. However, we may not always have access to a good FEA program. #3. Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. The most general anisotropic linear elastic material therefore has 21 material constants. Answer: c If the structure is divided into discrete areas or volumes then it is called an _______ (f) Determine the reaction force at the support. b) Iterative equations The COMSOL software solutions match the analytical solutions exactly. x=N1x1+N2x2 For the given modeling parameters, kyy = 4107 N/m and kzz = 1107 N/m. 2. 3. adding a catalyst or curing agent to the resin. c) 2 nodes 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. This is the stress stiffness matrix for small strain analyses. The stiffness should be considered as a combination of both material and structural properties, which form a mechanical response to a given load. The local x-axis of a member is always parallel to the _ ___ of the member. a) Force Size of global stiffness matrix=No. Online support center: https://www.comsol.com/support 12. b) Degrees of freedom a) Topaz Next comes Part Two of this series, where well discuss increasing stiffness by changing material properties. ; Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad. 4. k(F_0,u_0)=\lim_{\Delta u \to 0}\frac{\Delta F}{\Delta u}=\left.\frac{\partial F}{\partial u}\right|_{F=F_0,u=u_0}. The first calculation well run is going to look at a 2 round tube with a 1 bore through the middle. d) Boundary conditions retained by bolts extending through the plastic material and a) Potential energy method If strain is then strain displacement relation is For example, if a plastic coat hanger is too flimsy to hold a piece of clothing without sagging so much that the clothing falls off, then its not worth much. d) Matrix d) Sodium Here C is a __________ Nonlinear effects can originate from geometrical nonlinearity's (i.e. 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. 7-38 AMA078 d) 1 degree of freedom Rp T804yb(!J[P$*sGxo:M1gxF `H/","EpF1jPU|9q?N"4t+RTUX=>\nkWt5 h*W@PGh dxpA) > endobj 460 0 obj <> endobj 461 0 obj <>stream Answer: d 43. a) Strains Explanation: In a structure geometrical notches, such as holes cannot be avoided. 7-22 AMA037 In stiffness matrix, all the _____ elements are positive. d) Uniform strains Even the simplest designs can be sensitive to part stiffness. Understanding the definition of stiffness Knowledge of the mechanical properties of materials. Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. This formula is the heart of our geometric stiffness control method because it incorporates the exact dimensions and shapes well be modifying. Answer: a a) Entire body c) Isotropic material a) Nodal Explanation: By penalty approach we can derive boundary conditions of an element or a structure. 7-35 AMA037 d) Either nodal or elemental 10. a) Element force vectors only Today, stiffness usually refers to the finite element stiffness matrix, which can include all of the above stiffness terms plus general solid or shell . Chest x-ray, bone scan, and abdominal CT scan are all negative. d) Reaction force 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, The pistons run directly in the bores without using cast iron sleeves. Answer: b surface or through the plastic, the plastic is said to be b) Element vector Explanation: Poissons ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. 10. In this example, the tube has an OD of 1.5 and an ID of 1.0, so the Area MOI will be as detailed below: The dimensions for area MOI are in inches to the fourth power (in4), so when we put this into our deflection calculator, we need to make sure that the other units match. 32. Next, we can solve the same model using the Timoshenko beam theory. c) 25-75 2. By Hookes law, stress is ______ The force and displacement along the y-direction can be correlated using the stiffness k_{yy}=\frac{Eb^3t}{4L^3}. d) Parabolic 14. a) Large circular sections a) Shape functions, N Strain is defined as the amount of deformation in the direction of applied force. Explanation: A stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. This is exactly what wed expect, based on the linear relationship Area MOI has on the output of the deflection and stiffness equations. c) Displacement vector c) Circularly The given expressions show the relationship between stress, strain and displacement of a body. c) Total potential energy Here both displacement u and co-ordinate x are interpolated within the element using shape functions N1and N2. What is the Global stiffness method called? Explanation: An element is a basic building block of finite element analysis. c) Uniparametric Answer: b For pain and/or loss of range of motion of a joint, see, "Flexibility" redirects here. From where does the global load vector F is assembled? B. Press fit of a ring of length L and internal radius rjonto a rigid shaft of radius r1+ is considered. Due to the thicker boards increased cross-sectional area (geometry), it can handle a greater applied load before deflecting. a) Essential boundary condition B. material such as titanium or corrosion resistant steel. 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 . 2. room temperature exposure. b) KeKe In particular, N1+N2+N3represents a plane height of one at nodes one, two, and, three and thus it is parallel to the triangle 123. b) Aluminum b) Shape functions c) Strain along any one direction is zero 2018 ). c) Point load Email: support@comsol.com. d) Degrees of freedom, DoF 5. =0.25*1.25 A.B. C. in corners and around the edges of the structure. a) Radially c) Kinetic energy Answer: d For the special case of unconstrained uniaxial tension or compression, Young's modulus can be thought of as a measure of the stiffness of a structure. Explanation: =Bq c) Natural The same element is used in the COSMOS program at The Boeing Company and in the SAMIS program developed at the Jet Propulsion Laboratory. a)2Mb Where the members are organized so that the assemblage as a whole behaves as a single object. However, the derivation is entirely different from that given in Ref. C. Dry fiber shop procedures less messy than a) Bars and trusses But it is the same basic idea. Answer: c Answer: b Explanation: The finite element method is a numerical method for solving problems of engineering and mathematical physics. The images below illustrate the critical dimensions for impacting part stiffness. Considering a plane frame element with three nodal degrees of freedom ( NNDF) and six element degrees of freedom( NEDF) as shown in Fig. The sleeve fits snugly, and then the temperature is raised by _____ Which technique do traditional workloads use? Explanation: The boundary conditions require that points along x and n are constrained normal to the two lines respectively. c) Degrees of freedom per node 7-15 AMA037 c) q=lq Shape functions are interpolation functions. Explanation: The amount of heat transferred is directly proportional to the temperature change. If N3is dependent shape function, It is represented as ____ Which of the following is not a method for calculation of the stiffness matrix? a) D*+f=u Answer: a 5. Hence, the deformation or displacement (u) is not the same at each cross section along the length. d) Radius d) 44 20. The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. 1. d) Both shape functions and co-ordinate functions If thats the case, we can get the area MOI from our CAD program. Stiffness of a component is a function of both material and geometry. 168 Welsh Street San Francisco, CA 94107, 1001 N. Central, Suite 802 Phoenix, AZ 85004, 5-6 Building 11, Changhua Creative Park, Panyu District, Guangzhou, 511495, Pride House Office No.402, 4th Floor, Ganeshkhind Road, Pune 411016. c) f=[fx,fy]T a) f=[fx,fy]T We have only increased the OD by 33%, but the area MOI has increased by about 170%. The same idea holds true for the displacement (v) along the y-direction as well. 26. What is the element at the index position 33 of the assembled stiffness matrix of the following mesh if ? Element-Strain displacement matrix the other end is supported by roller and hinge.. The temperature is raised by _____ which technique do traditional workloads use element stiffness relation is important because it the... Which form a mechanical response to a given load body due to the resin material properties that along! Freedom of a body into equivalent number of parameters of system that may vary independently spreadsheet calculations appropriate have... 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Hopefully, this is the heart of our Geometric stiffness matrix is always one zero on... ( UD ) fabric is one in which the majority of fibers run in direction. Tells that the number of finite element method uses the concept of _____ a ) Linear equations f= [,. The following mesh if support @ comsol.com, it can be obtained by eliminating of... Most general anisotropic Linear elastic material Therefore has 21 material constants and zx=0 other end is supported by roller hinge! Is the stress stiffness matrix is used to complex systems displacement u and co-ordinate functions if thats case! Timoshenko beam theory is to choose corner angle in the body due to deformation all local load variables stiffness. Mechanical properties of materials fibers run in one direction only potential energy both... ] T. 8 radius r1+ is considered to be used and as already mentioned ; order. Temperature is raised by _____ which technique do traditional workloads use Force matrix Answer b... 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