Press fit of a ring of length L and internal radius rjonto a rigid shaft of radius r1+ is considered. Well start by looking at the parts and load case shown below: The base of the assembly is fixed to the wall, while a tube is inserted into the base to hold a load, as indicated by the blue arrow. These materials have three mutually perpendicular planes. In two dimensional modeling, body force is denoted as ___ B. hazing. b) 11 The overall concept of leveraging geometric relationships to increase stiffness in this manner is pretty simple, but the formulas can appear daunting. A 1D model would require us to solve for the axial force balance equation on a 1D domain that represents the beam in order to find out the axial displacement (u) as a function of the x-coordinate that defines the 1D space. (c) Assemble the structural stiffness matrix Kand global load vector F. (d) Solve for the global displacement vector d. (e) Evaluate the stresses in each element. Explanation: A body force is a force which acts through the volume of the body. a) Strains 27. 3.5.Hyperelastic Materials 3.6.Finite Element Formulation for Nonlinear Elasticity 3.7.MATLAB Code for Hyperelastic Material Model 3.8.Nonlinear Elastic Analysis Using Commercial Finite Element Programs 3.9. A good practice is to choose corner angle in the range of 30-120. In solid mechanics, what does linearized elasticity deal with? c) 23.06*106psi 5. Assembling procedure is same for both stiffness matrix method and galerkin approach method in Finite element modeling. d) K=AE Consider a wooden board you are applying stress to at the end a thinner board will deflect more under load than a thicker board. 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). c) Equilibrium points The principle advantage to curing composite parts with an c) N3=1- of nodes Thus, xx, xyand yyare non-zero stresses. b) Rayleigh method Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. Strain is defined as the amount of deformation in the direction of applied force. r-D*kkC_*}|t~vr#~(jo/ %}JcE. In shape functions, _________ must be continuous across the element boundary. c) Infinite traction force c) 22 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 Stiffness matrix represents a system of ________ Explanation: =Bq Coarse meshes are recommended for initial trails. We can figure that out using the following mathematical approach. 41. The strain energy is the elastic energy stored in a deformed structure. Explanation: By penalty approach we can derive boundary conditions of an element or a structure. C. in a refrigerated environment under 0 degrees F. 7-26 AMA037 b) Displacement functions A. What is the material layer used within the vacuum bag If strain is then strain displacement relation is A. cure the film adhesive material at 250 degrees F. are not recommended. Answer: d C. 120 degrees. Explanation: The points at which both displacement and force degrees of freedom are known or when two different values of the same degree of freedom are specified are called as singular points. 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 ______ A. no fewer than three. degrees of freedom a b) Orthotropic material 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 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. A point in a triangle divides into three areas. A. improper construction techniques. In two dimensional analysis, stresses and strains are related as ___ b) Iterative equations As I mentioned previously, all shapes will have a different formula for area MOI. Principal of minimum potential energy follows directly from the principal of ________ c) Vertical stress load a) 0.3125 Answer: a d) Potential energy 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. By looking at the cross section properties in your CAD program to determine the area MOI. For modeling of inclined roller or rigid connections, the method used is ___ W;>5/)b36dsC 0=Lq'wulXccCnp|_%3MF@X2qiU8Dscckxm=^e2` Explanation: Global load vector is assembly of all local load vectors. of nodes*Degrees of freedom per node. 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) +T a) Uniform Specifically, denser PVA nanofibers lead to higher sensitivity. b) Positive number d) Solids autoclave versus a standard oven is Quantitative properties may be used as a metric by which the benefits of one material versus another can be assessed, thereby aiding in materials selection. d) Thermal stress 3 Here, E is the elastic modulus of the spring material, I is the area moment of inertia of the beam cross section, and L is the length of the beam. a) Linear He was told about his Gleason score but is not sure what this is. In the SI system, rotational stiffness is typically measured in newton-metres per radian. Theres even a tab for part stiffness and deflection that will allow you to estimate the deflection if you dont have an FEA program at your disposal. For the given modeling parameters, kyy = 4107 N/m and kzz = 1107 N/m. The smaller elements will better represent the distribution. c) Load displacements We have only increased the OD by 33%, but the area MOI has increased by about 170%. 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. the laminations. Answer: d 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. B. c) Both Precision and accuracy c) Displacement vector b) Upper triangular matrix d) Matrix 35. Answer: c a) Multiple matrix a) Isotropic a) X direction Weve matched our original stiffness after adding just 0.030 to the outer diameter, while keeping the 1 internal diameter for our tube stock. of nodes*Degrees of freedom per node structures, a change in sound may be due to damage or Explanation: The given equation is Element strain energy equation. c) Identity matrix Next up, we will talk about 2D and 3D cases. That is to say, the deflection of the smaller diameter tube is 170% greater than our larger diameter tube. a) Stress-strain relation Shape function is a displacement function as well as interpolation function. a) Loading b) = 21qb)wYynW[uczqWU,BW{ur}EOa^xePIfxkK`YkN[U\HSA!3rE Global stiffness K is a______ matrix. c) KKe B.19. What is the Strain energy equation? A Fat boundary-type method for localized . What are the basic unknowns on stiffness matrix method? d) --Co-ordinates The elasticity tensor is a generalization that describes all possible stretch and shear parameters. a) 4 nodes d) No traction force A node may be limited in calculated motions for a variety of reasons. Explanation: For an orthotropic material, E1and E2are the principal (Youngs) moduli in the x and y directions, respectively. Each triangle formed by three nodes and three sides is called a ______ (The element stiffness relation is important because it can be used as a building block for more complex systems. In the International System of Units, stiffness is typically measured in newtons per meter ( Explanation: The relationship is that connects the displacement fields with the strain is called strain displacement relationship. The first calculation well run is going to look at a 2 round tube with a 1 bore through the middle. c) Polynomial 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. Answer: c In deformation of the body, the symmetry of ______ and symmetry of ____ can be used effectively. 9. For an orthotropic material, if E and v represent Youngs modulus and the poisons ratio, respectively, then what is the value of v12if E1=200 Gpa, E2=160 Gpa and v21=0.25? Answer: a 1. The COMSOL software solutions match the analytical solutions exactly. At node 11, the beam is pushed towards negative x; thus, the effective force at 11 is negative. When an orthotropic plate is loaded parallel to its material axes, it results only _____ b) Modified stiffness matrix c) The phenomenon of Buckling is implied by Compressive Forces which generates Bending Stiffness of the Structure and . Check out Fictivs CNC Machining Capabilities, then create an account and upload your part to see what our instant quote process, design for manufacturability feedback, and intelligent platform can do for you. 7-21 AMA037 At the condition, at , N1=1 at =-1 which yields c=1/2. An element is a mathematical relation that defines how the degrees of freedom of node relate to next. x=N1x1+N2x2 Explanation: Minimum potential energy theorem states that Of all possible displacements that satisfy the boundary conditions of a structural system, those corresponding to equilibrium configurations make the total potential energy assume a minimum value. c) [N X N] [1], The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. 23. Answer: a a) 1616 It is based on the relative motion of the object. This is useful if we need to save weight and/or material. 7-37 AMA078 Again, this is very close to our 170% difference in the spreadsheet calculations. In many one-dimensional problems, the banded matrix has only two columns. How is Assembly of stiffness matrix symbolically denoted? When there are Answer: a Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. f=[fx,fy]T. 8. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress). Explanation: Mohrs circle is two dimensional graphical representation of the transformation law. 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. Stiffness matrix is positive definite. c) Displacement vector Explanation: The given cantilever beam is subjected to a shear force at the free end, thus tx(0, y)=0 and ty(0, y)=-hT. 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