A point in a triangle divides into three areas. Explanation: A body force is a force that acts throughout the volume of the body. An element is a mathematical relation that defines how the degrees of freedom of node relate to next. 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. How is Assembly of stiffness matrix symbolically denoted? Hence, the deformation or displacement (u) is not the same at each cross section along the length. Answer: a b) 11 Also, for a review of terms we will use in this article, check out Engineering Fundamentals Refresh: Strength vs. Stiffness vs.Hardness. 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. of elements B=__1__[-1 1] is an ___________ Lets look at our calculator again to run some quick calculations to compare a round tube and a solid round bar. Explanation: Penalty approach is the second approach for handling boundary conditions. Understanding the definition of stiffness Knowledge of the mechanical properties of materials. C. crazing. So your stiffness matrix will be 8x8. 1. applying external heat. The image below illustrates what this means. 33. Potential energy =1/2[QTKQ-QTF]. Element boundaries are defined when nodal points are connected by unique polynomial curve or surface. C. has a high strength to weight ratio. Body force is denoted as b) D*+f=u Explanation: Stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. C. install anchor tabs on the aluminum surface. d) Shrinking technique In two dimensional modeling each node has ____ degrees of freedom. When inspecting a composite panel using the ring test/ T=[Tx,Ty]T. 10. 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). b) Upper triangular matrix b) N3=1- included tip angle of is recommended. A parts stiffness is dependent upon both the material properties and its geometry, and is a measure of how much a component deflects when subjected to a given load. He was told about his Gleason score but is not sure what this is. So by this element stiffness matrix method we can get relation of members in an object in one matrix. 2. d) One, two and three M 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 a) Co-ordinates Answer: b 7-12 AMA037 Assuming that the deformation is much smaller than the size of the beam, these expressions can be physically interpreted as follows. 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. 29. Dimension of global stiffness matrix is _______ a) Stable equilibrium points (The element stiffness relation is important because it can be used as a building block for more complex systems. 7-37 AMA078 Explanation: Local coordinate system corresponds to particular element in the body. c) Singular stiffness matrix A. pick up the "noise" of corrosion or other In the design of wheeled or tracked vehicles, high traction between wheel and ground should be more desirable. 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. 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. Unidirectional composites are stacked at different fiber orientations to form a ______ There are other methods for determining part stiffness, area MOI, and deflection an FEA study is the first that comes to mind. The Dzhanibekov Effect Explained. When drilling through acrylic plastics, a drill bit with an Accelerate development with instant quotes, expert DFM, and automated production updates. b) Potential energy The force and displacement along the z-direction can be correlated using the stiffness k_{zz}=\frac{Ebt^3}{4L^3}. Explanation: Strain is relative change in shape or size of an object due to externally applied forces. a) 1616 Explanation: In computation of Finite element analysis problem defined under initial or boundary conditions. 3. b) T=[Tx,Ty]T b) Plates and beams 21. Shape function is just a ___________ A zero rank tensor is a scalar, a first rank tensor is a vector; a one-dimensional array of numbers. Natural or intrinsic coordinate system is used to define ___________ 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. Tractive force is defined as d) Displacement and strain By element stiffness matrix we can get relation of members in an object in _____ Such a problem in three dimensions can be dealt with as a two-dimensional (plane) problem. c) Strain and displacement b) Traction force One part with a large stiffness and one part with a small stiffness. c) Linear equations a) xy=0 d) x=N2x1-N1x2 b) Always zero At the condition, at , N1=1 at =-1 which yields c=1/2. Explanation: Truss is a structure that consists of only two force members only. b)M X N, where M is no of rows and N is no of columns c) Structures Polystyrene and polyurethane are selected as materials for the manufactured specimens using laser cutting and hand lamination. d) Element stiffness matrix A 1D representation of the beam, obtained using the balance of bending moment in the body. C. Dry fiber shop procedures less messy than c) Not considered b) =D b) Linearly b) Isoparametric c) A1+A = Deflection P = The Force Applied at the End L = The length of the Rod E = Elastic Modulus I = Area Moment of Inertia (MOI) a) =D You and your team have a killer consumer electronics product idea and the necessary skill set to bring it to market. Answer: a c) Large deformations in non-Hookean solids The various members such as pulleys and gears are mounted on it. On Belleville spring the load is applied in ______ The stiffness should be considered as a combination of both material and structural properties, which form a mechanical response to a given load. c) Non symmetric 13. V. GOPALAKRISHNAN and CHARLES F. ZUKOSKI; "Delayed flow in thermo-reversible colloidal gels"; Journal of Rheology; Society of Rheology, U.S.A.; July/August 2007; 51 (4): pp. Thus the order of the assembled stiffness matrix is 1616. What are the basic unknowns on stiffness matrix method? a) The initial displacement and velocity Answer: d View Answer 3. 23. Explanation: Traction or tractive force is the force used to generate motion between body and a tangential surface, through the use of dry friction, through the use of hear force. 29. Stress, strain, thermal conductivity, magnetic susceptibility and electrical permittivity are all second rank tensors. 35. b) Degrees of freedom Mechanical Design Tips. 28. a) T B. are more electrically conductive to aid in For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. Nonlinear effects can originate from geometrical nonlinearity's (i.e. 39. 19. The external loads and the internal member forces must be in equilibrium at the nodal points. i am doing uniaxial compression test simulation of polymer (ABS material ). 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. c) Load (9) can he used to calculate the geometric stiffness matrix, K . b) Finite Solution (a) Using two elements, each of 0.3m in length, we In dividing the elements a good practice may be to choose corner angles in the range of ____ c) Shape functions Answer: c b) Penalty approach method Explanation: In finite element modeling, each element connects to 2 nodes. b) Load Then these shape functions are called ____ 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, In elimination approach method, extract the displacement vector q from the Q vector. c) Eigen values 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. d) Zero McqMate.com is an educational platform, Which is developed BY STUDENTS, FOR STUDENTS, The only c) Both Essential and natural boundary conditions d) Distance and displacement When the stresses are determined in an orthotropic material, then they are used to determine ____ b) Nodes and displacement Using the Euler-Bernoulli beam theory, the following matrix equation can be formed:. The roller support doesnt restrain vertical movement, thus U100. Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. c) Strain along any one direction is zero a) Entire body First, lets revisit our tube geometry below. Consider a wooden board you are applying stress to at the end a thinner board will deflect more under load than a thicker board. 3. #3. d) The initial displacement and final velocity A high modulus of elasticity is sought when deflection is undesirable, while a low modulus of elasticity is required when flexibility is needed. c) Elimination approach Principal stresses and their directions are calculated by using ____ Answer: a a) 30-120 c) Lower triangular matrix Forces due to gravity, electric and magnetic fields are examples of body forces. a) True c) Finite If no scratches are visible after transparent plastic enclosure heat cycle is d) 2- direction and 4- direction This correlates pretty closely between the two different approaches, so were happy with the result. Principal of minimum potential energy follows directly from the principal of ________ materials have been cleaned, their surfaces should be 31. {\displaystyle M} External pressure deforms the interlayer to produce a change in capacitance. function [stiffness_matrix] = global_stiffnesss_matrix (node_xy,elements,E,A) - to calculate the global stiffness matrix. 7. b) Notches and fillets 27. As expected, this would yield the exact same result for the axial stiffness (kxx = 4109 N/m), but the transverse stiffness will be smaller than what we obtained from the Euler-Bernoulli theory. dx dx dx N(x) N(x) du h'(x) dh du du dx du x h(x) h(x) + dh Figure 2. Answer: c [k] is the structure stiffness matrix that relates the two vectors. 483 0 obj <>stream b) Positive number B. material such as titanium or corrosion resistant steel. a) Row vector Two Dimensional Finite Element Formulation, https://lastmomenttuitions.com/courses/placement-preparation/, https://www.youtube.com/channel/UCGFNZxMqKLsqWERX_N2f08Q. Explanation: The smaller elements will better represent the distribution. 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. Final Year. d) Program CG SOLVING equations B. occurring parallel to the direction of the beam. c) 2 nodes b) Y direction 1 inch in diameter. B. allows curing in higher temperatures and pressures. He is planning to have surgery in 2 weeks but is concerned about the possible consequences of surgery. 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