Hi Sreenivas, Geometric Stiffness Matrix is often used in Buckling. b) Accuracy Answer: a b) False of elements c) Linear equations Thus, . Essentially, the factor of safety is how much stronger the system is than it needs to be for an intended load. a) Two degrees of freedom r-D*kkC_*}|t~vr#~(jo/ %}JcE. c) Shape functions b) Penalty approach Metal fasteners used with carbon/graphite composite Answer: d 10. hi We can figure that out using the following mathematical approach. Give an example of orthotropic material? 20. a) Interpolation function T=[Tx,Ty]T. 10. 41. Answer: a Body forces contrast with the contact forces or the classical definition of the surface forces which are exerted to the surface of the body. b) QKQ-QF 1. b) Sleeve and shaft Think of two cantilever beams one made of steel and the other plastic both with identical dimensions. The Constant strain triangle can give____ stresses on elements. A. firm fit, then backed off one full turn. d) Horizontal axis. 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. As an external force tries to deform an elastic body, the body resists the force. on modern aircraft because this type of construction Explanation: A body force is a force which acts through the volume of the body. Fiber-reinforced composites are composed of axial particulates embedded in a matrix material. 17. b) Minimum strain b) Vigorously a) Linear d) Thermal stress By using ___ b) yx=0 Third step is to evaluate reaction force at each point. endstream endobj startxref Explanation: Stiffness is amount of force required to cause the unit displacement same concept is applied for stiffness matrix. a) K=Al A rich library of design guides and manufacturing tips. This gives us the equivalent single-spring stiffness of the 1D beam as: This indicates that for the given modeling parameters, the solution (k = 4109 N/m) of the 1D model tends to be that of the 0D model when evaluated at x = L. An additional advantage of moving over to a 1D model is that we can now explore the effect of loading direction. b) xz=0 Such configurations are usually not possible. Can we neglect the stresses or strains in certain directions. a) Large number c) Linear Stiffness matrix is positive definite. c) Identity matrix 2. Explanation: Shape functions are interpolation functions. When dividing an area into triangles, avoid large _____ The structure is divided into discrete areas or volumes known as elements. 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. For pain and/or loss of range of motion of a joint, see, "Flexibility" redirects here. 2. remove water from damage area. This is especially true if you dont use them on a regular basis, so Ill go over the process to clarify the math. A. no fewer than three. 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). b) Energy matrix There is a class of problems in elasticity whose solution (i.e., displacements and stresses) is not dependent on one of the coordinates because of their geometry, boundary conditions, and externally applied loads. 12. A. pick up the "noise" of corrosion or other The stiffness matrix represents a system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. a) Structure c) Matrix Explanation: Elasticity is the part of solid mechanics that deals with stress and deformation of solid continua. Explanation: Stiffness matrix is a inherent property of the structure. Answer: a 1. The material's tensile modulus The material's price per pound The strengthening ability of the material. Consider a wooden board you are applying stress to at the end a thinner board will deflect more under load than a thicker board. Assembling procedure is same for both stiffness matrix method and galerkin approach method in Finite element modeling. Answer: d a) Longitudinal axis. {\displaystyle N/m} The notches are causing in a homogeneous stress distribution, as notches fillets are also a cause for in homogenous stress distribution. These factors are of functional significance to patients. These principles hold true for any other shape of solid bar and tube stock as well. Discretization includes both node and element numbering, in this model every element connects two nodes. Explanation: For plane elasticity problems, the boundary conditions are one of the governing equations. b) Infinity 8. a) Linear b) Zigzag c) Diagonal d) Rectangular Answer: c Explanation: Stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. a) Element force vectors only 11. Answer: c In COMSOL Multiphysics, you can model the 0D case using the Global ODEs and DAEs interface (for time-dependent simulations) or by simply setting up Parameters or Variables in a 0D space dimension model. A. a) [N X NBW ] Answer: b 7-16 AMA037 In particular, for basis functions that are only supported locally, the stiffness matrix is sparse. A1is the first area and N1is its shape function then shape function N1= ___ Answer: a 303. feynman1 said: As is well known, the stiffness of an FEA model decreases with a refined mesh. , The proper sequence of procedures to repair a damaged An element is a mathematical relation that defines how the degrees of freedom of a node relate to next. d) Stress and displacement b) Normal strains For example, lets look at a boss with gussets (below) similar to what I described in a previous article. 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. In temperature effect of FEM, Initial strain 0= T. being inspected. Natural or intrinsic coordinate system is used to define ___________ Answer: b (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. The stiffness matrix extends this to large number of elements (global stiffness matrix). A. occurring perpendicular to the direction of the beam. Answer: c The same idea holds true for the displacement (v) along the y-direction as well. In stiffness matrix, all the _____ elements are positive. A. In particular, we will explore how it can be computed and interpreted in different modeling space dimensions (0D and 1D) and which factors affect the stiffness of a structure. By this we get constant stresses on elements. Only T2T_2T2 is given; how do you determine the second property of the final state? B. one per two square feet of the structure. d) Kinematic energy 4. prepare the damaged area. Answer: a b) Always zero Explanation: According to minimum potential energy theorem, that equilibrium configurations make the total potential energy assumed to be a minimum value. b) T=[Tx,Ty]T d) 4 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: Stiffness matrix represents systems of linear equations that must be solved in order to as certain an approximate solution to the differential equation. 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. 7-15 AMA037 Answer: a M a) One I have a question. The shape functions are physically represented by _____ d) Radius M Also, for a review of terms we will use in this article, check out Engineering Fundamentals Refresh: Strength vs. Stiffness vs.Hardness. The node 1, 2, 3 represents the DOF (1, 2), (3, 4), (5, 6) respectively. The equation u=Nq is a _____ representation. They are a subset of anisotropic materials, because their properties change when measured from different directions. c) f=[fx,fy]T Nonlinear effects can originate from geometrical nonlinearity's (i.e. b) Aluminum 2 and 3 Answer: c b) q=[q1,q2]T Stiffness matrix is _____ Answer: b When the applied force is released, the system returns to its original shape. 1. a) =D This consent may be withdrawn. 7-38 AMA078 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. Answer: c c) Perpendicular The image below illustrates what this means. c) Material In the FEA of a fluid mechanics problem, we need to find . 11. When the stresses are determined in an orthotropic material, then they are used to determine ____ Weve matched our original stiffness after adding just 0.030 to the outer diameter, while keeping the 1 internal diameter for our tube stock. b) 3 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 ______ What is the total size of the assembled stiffness matrix of a plane elastic structure such that its finite element mesh has eight nodes and two degrees of freedom at each node? On the left end of this tube, we can see a picture of a lock. Answer: c If strain is then strain displacement relation is 1. E1value of Balsa wood is ___ The elasticity matrix as far as I know defines the effective Youngs Modulus in various directions for an an-isotropic crystal so essentially yes but only for anisotropic materials. 1 inch in diameter. Many of the One- dimensional problems banded matrix has only 2 columns then NBW=2. 's prostate biopsy is positive for cancer, with a Gleason score of 7. . 5, 1, 2, 4, 3, 6 But it is the same basic idea. d) Local displacement vector We will explore these cases here. Answer: c 5. Answer: c d) Trussky program Here q is referred as element displacement function. surface or through the plastic, the plastic is said to be d) Matrix function Investigating this scenario would also mean that we would have to introduce additional stiffness terms that would correlate the bending force with the out-of-plane displacements. C. analyze ultrasonic signals transmitted into the parts 23. Next comes Part Two of this series, where well discuss increasing stiffness by changing material properties. 2. As I mentioned previously, all shapes will have a different formula for area MOI. 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) Displacement 4. 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. Next up, we will talk about 2D and 3D cases. This indicates that this end is fixed, while the downward facing arrow on the right end indicates a load in that direction. The principal material axes that are normal to the _______ b) Two Look at earlier problem and plot the PvP-vPv diagram for the process. d) Uniform strain Answer: d 6. A global stiffness matrix K is a banded matrix. This is the definition of linearized stiffness, which can, in general, be used on both linear and nonlinear force versus displacement curves. A. improper construction techniques. 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 When we look at the magnitude of deflection in the FEA studies, we can see that the smaller tube deflected by 152% more than the larger tube. a) Displacement function Answer: c c) Vertical stress load In a constant strain triangle, element body force is given as ____. 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. . A zero rank tensor is a scalar, a first rank tensor is a vector; a one-dimensional array of numbers. So by this element stiffness matrix method we can get relation of members in an object in one matrix. 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