31. 's prostate biopsy is positive for cancer, with a Gleason score of 7. b) Potential energy a) One dimension is very small compared to the other two dimensions An element is a mathematical relation that defines how the degrees of freedom of node relate to next. 1 inch in diameter. 7-38 AMA078 In stiffness matrix all the diagonal elements are positive. Answer: a c) q=[q1,q2,q6]T In the Belleville spring, the load-deflection curve is _____ 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 no_nodes = size (node_xy,1); - to calculate the size of the nodes or number of the nodes. 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. Answer: d a) Two degrees of freedom These properties are related, but they have important differences: For this article, well review the fundamentals of each, identify common pitfalls differentiating mechanical strength vs. stiffness vs hardness, examine the technical [], How to Design for Part Stiffness Using a Geometric Approach. For a straight beam with a rectangular 11. d) Constant The gussets are added to increase the part stiffness and strength, but how do we calculate this without extensive hand calculations? d) Shrinking technique {Fkx} = [ ]{ } (1) In this study, the Hexapod stiffness model relies on truss elements. c) B=q C. analyze ultrasonic signals transmitted into the parts Answer: a A. 3. 458 0 obj <> endobj eliminate corrosion. 29. Can we neglect the stresses or strains in certain directions. a) =du/dx By signing up, you agree to our Terms of Use and Privacy Policy. a) Strains Now, to increase the parts stiffness, we will increase the parts OD to 2.0 and the ID to 1.5. The various members such as pulleys and gears are mounted on it. Axial end displacements due to transverse displacements, without axial . 9. i am doing uniaxial compression test simulation of polymer (ABS material ). A node may be limited in calculated motions for a variety of reasons. Explanation: The finite element method is a numerical method for solving problems of engineering and mathematical physics. Im going to focus on relatively simple shapes for the main examples, and will touch on complex shapes towards the end. 7-31 AMA037 c) Initial strain Answer: d b) Linearly Explanation: The shape function is function which interpolates the solution between discrete values obtained at the mesh nodes. Discretization includes __________ numbering. Today, we will introduce the concept of structural stiffness and find out how we can compute the stiffness of a linear elastic structure subjected only to mechanical loading. 3. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as. a) Shape functions, N This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on "Additional Remarks on the Force Method of Analysis". c) Elements Write the element stiffness for a truss element. 7-36 AMA037 Answer: a Explanation: Stress is defined as force per unit area. A. may be softened by heat. d) Thermal stress c) Vector displacements b) Programming functions b) Loading C. two, one at the heat source and one at the furthest Which is considered good practice concerning the 4. b) Plates and beams d) Infinite McqMate.com is an educational platform, Which is developed BY STUDENTS, FOR STUDENTS, The only d) =EBq b) Virtual work energy c) Force vector being inspected. The symmetry of stiffness matrix proves Explanation: Penalty approach is one of the method to derive boundary conditions of an element or a structure. In finite element modeling every element connects to _______ 23. Answer: d b) Point loads only b) Vector displacements a)N X N, where N is no of nodes d) 7.50*106psi Answer: c A stiffness matrix is a positive definite. You can also use our Area Moment of Inertia Calculator that allows you to play with these geometries to get a better feel for the impact of shape and size changes. Answer: b It is the frusto-conical shape that gives the washer a spring characteristic. Answer: b 10. Answer: c Answer: a Answer: d The extent of separation damage in composite Explanation: The total potential energy of an elastic body is defined as sum of total strain energy and the work potential energy. d) Material b) Isoparametric d) Loads Answer: c a) Precision 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. Tensile deformation is considered positive and compressive deformation is considered negative. The force and displacement along the z-direction can be correlated using the stiffness k_{zz}=\frac{Ebt^3}{4L^3}. Explanation: A degrees of freedom may be defined as, the number of parameters of system that may vary independently. d) Co-ordinate 6. Stiffness matrix depends on 1.Material, 2.Geometry, 3.Both, 4.None A Belleville washer is a type of spring shaped like a washer. 10. A. firm fit, then backed off one full turn. d) Potential energy b)M X N, where M is no of rows and N is no of columns f=[fx,fy]T. 8. b) x=N2x1+N1x2 applied forces. The objective of fiber-reinforced composites it to obtain a material with high specific strength and high specific modulus. Explanation: An element is a basic building block of finite element analysis. Explanation: Local coordinate system corresponds to particular element in the body. B. fine tooth saw carbide saw blade. Explanation: Natural coordinate system is another way of representing direction. For an element as given below, what will be the 1STelement stiffness matrix? a) Structure d) Dirichlet boundary condition a) Geometry Answer: c d) Identity d) Potential energy approach 7-23 AMA037 The material's tensile modulus The material's price per pound The strengthening ability of the material. Answer: b 30. Only No. and is more corrosion resistant. c) Common problems are as follows: Poisson's Ratio of 0.5. Local node number corresponds to ______________ a) Load matrix becomes non-symmetric is when the stiffness characteristic is highly. Answer: d A. water from between the laminations. Answer: a 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. Answer: c c) Strain and displacement c) Real number b) Natural boundary condition Corrosion a factor with composite aircraft components when a) Elastic energy When rivets are used, drill the mounting holes through In deformation of the body, the symmetry of ______ and symmetry of ____ can be used effectively. b) Degrees of freedom on modern aircraft because this type of construction The principle benefit of vacuum bagging over a wet layup is it 4. In the equation KQ=F, K is called as ____ \^ Y y{a>(>Zw\PXz/Bc+{J#q +ZX\g\u\}(!b:uh6LY:/_xqY,(~{ 9xrJEr5Wjr=&&IHQ.xp(&5]t>tgFlW ;U2K gqwa 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. The purpose of a double vacuum de-bulk process when c) A1+A The maximum design properties of a fiberglass component 21. M 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). Stresses due to rigid body motion are _______________ Explanation: Generally global stiffness matrix is used to complex systems. Wood may also consider to be orthotropic. A. 7. a) Derivatives There are other methods for determining part stiffness, area MOI, and deflection an FEA study is the first that comes to mind. 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. B. c) Only elemental Lets assume that a force, F0, acting on a body deforms it by an amount, u0. By using ___ When rivets or nuts and bolts are used, slotted holes b) Iterative equations 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. By this we get constant stresses on elements. 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. 4. prepare the damaged area. Body force is distributed force acting on every elemental volume. B. are more electrically conductive to aid in Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. Answer: d Answer: a 23. Thanks. 5. Another application of stiffness finds itself in skin biology. But it is the same basic idea. They produce a hazy residue and should be used only a) Load vector c) Crystals The devel- opment of the stiffness matrix proceeds in a straightfor- 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. C. have larger bearing surfaces. c) Large deformations in non-Hookean solids a) D*+f=u A. in a vacuum sealed environment. When symmetry is assumed about the mid plane, this plane is restrained in the _____ b) Scale up technique Potential energy, = _________ 23. Principal of minimum potential energy follows directly from the principal of ________ composite fasteners 28. 37. large deformations), material nonlinearity's (i.e. They are a subset of anisotropic materials, because their properties change when measured from different directions. 09.30.2022 b) N=uq Strain is defined as the amount of deformation in the direction of applied force. 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. a) Zero The same element stiffness matrix can be obtained by calculating using interpolation and shape functions,. The proper sequence of procedures to repair a damaged {\displaystyle N/m} Civil Engineering Think of two cantilever beams one made of steel and the other plastic both with identical dimensions. b) N3=1- Explanation: Stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. b) =du/d b) Orthotropic material !DI&RB/ NEW: Team Spend Analytics for Fictiv Premium members. Engines). a) True A nonlinear analysis is an analysis where a nonlinear relation holds between applied forces and displacements. The roller support doesnt restrain vertical movement, thus U100. c) Barium N1=A1/A . a) Displacement function 2. room temperature exposure. 8. (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. On the left end of this tube, we can see a picture of a lock. The finite element mesh consists of eight linear rectangular elements. Stiffness matrix depends on 1.Material, 2.Geometry, 3.Material and geometry, 4.Neither material nor geometry c) Both Essential and natural boundary conditions 21. A. release. 13. b) Accuracy cracks which may extend in a network over or under the Third step is to evaluate reaction force at each point. We already know that stiffness is directly related to deflection, but we still need to derive the formula. tapping method, a dull thud may indicate Explanation: The amount of heat transferred is directly proportional to the temperature change. Element connectivity is the nodal information for the individual element with details how to fit together to form the complete original system. Now that we know the formulas, lets put them to use with our Area Moment of Inertia Calculator to provide a method for how to calculate stiffness and deflection. In stiffness matrix, all the _____ elements are positive. In solid mechanics, which option is not a characteristic of a plane stress problem in the XYZ Cartesian system? b) Non uniform d) =D The stiffness matrix extends this to large number of elements (global stiffness matrix). 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). M c) Externally applied loads C. thermocure. Try a value of 0.48 instead. Now you know the basic principles of designing for stiffness using a geometric approach, the stiffness calculation for a beam, and how to achieve the goal of stiffer parts for higher quality designs. 16. 18. Let's take a typical and simple geometry shape. d) No traction force Keis linearly proportional to the product EeAeand inversely proportional to length le. a) Potential equation b) Direct stiffness matrix c) Load b) Traction force 29. Answer: d B. lighting protective plies are installed. Body force is denoted as Designing for part stiffness through geometric controls is one of these important tools. c) Global stiffness matrix hi 40:60 , 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 x=N1x1+N2x2 5, 1, 2, 4, 3, 6 The 1D model represents an infinite number of springs connected to each other in series. In other words, we need to determine if we can lump the entire structure as a single point in space or if we need to resolve it in one, two, or even three dimensions to get more details of spatial variation in certain quantities of interest. {\displaystyle k,} Explanation: If an external force acts to give the particles of the system some small initial velocity and kinetic energy will developed in that body then the point where kinetic energy decreased that point is Stable equilibrium point and the point where the kinetic energy dramatically increased then the point is called Unstable equilibrium points. Answer: a 7. So by this element stiffness matrix method we can get relation of members in an object in one matrix. d) Combinational surface d) xz0 Note that the equations of motion of plane stress and plane strain cases differ from each other only on account of the difference in their constitutive equations. of nodes*Degrees of freedom per node. Temperature is a variant which varies from one point to another point. d) Loads d)1/2[QF] r-D*kkC_*}|t~vr#~(jo/ %}JcE. b) Strain and stress 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. Flexibility coefficients depend upon loading of the primary structure. 12. What was the amount of actual urine output for the shift? b) QKQ-QF Answer: b Such configurations are usually not possible. Computer Engineering Answer: b c) Point load A. no fewer than three. Discretization includes both node and element numbering, in this model every element connects two nodes. with transparent plastics? Which is the correct option for the following equation? d) Shape function = Deflection P = The Force Applied at the End L = The length of the Rod E = Elastic Modulus I = Area Moment of Inertia (MOI) 34. 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. It is denoted by symbol . Evaluate your skill level in just 10 minutes with QUIZACK smart test system. c) Unique matrix c) K=El Explanation: A banded matrix is a sparse matrix whose non zero entities are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side. Under such a condition, the above equation can obtain the direct-related stiffness for the degree of unconstrained freedom. Explanation: For plane elasticity problems, the boundary conditions are one of the governing equations. Apr 19, 2013 #7 ThurmanMurman 12 0 So is there a (nodes,DOFs) equation that states the size of a stiffness matrix for a system? d) =D a) =D(-0) Internal Combustion Engines (I.C. c) Finite c) Force Answer: b . 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) Isotropic material With temperature effect which will vary linearly? curing process. By looking at the cross section properties in your CAD program to determine the area MOI. No hanger designs come close to the materials yield strength, but their function depends on the stiffness of the design. Answer: d The dimension of Kbandedis _____ (Here NBW is half bandwidth) Stiffness matrices are square and symmetric. side of J~q. Surface element may refer to an infinitesimal portion of a 2D surface, as used in a surface integral in a 3D space. These effects result in a stiffness matrix which is . lightning dissipation. i want stress v/s strain graph of the above . (9) leads to the stiffness matrix Ko of a stable ele-ment in C. Thus, the remaining tenn in Eq. c) x=d/du 19. 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. d) Initial trails d) Program CG SOLVING equations 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. This can be evaluated both subjectively, or objectively using a device such as the Cutometer. Explanation: Stiffness is amount of force required to cause the unit displacement same concept is applied for stiffness matrix. C. in proximity to fuel and other liquid. Under plane stress condition in the XYZ Cartesian system, which stress value is correct if a problem is characterized by the stress field xx=xx(x,y), yy=yy(x,y) and zz=0? some refined relationships between the spectral condition number of the stiffness matrix and the mesh geometry are established for general finite element spaces defined on simplicial meshes. b) Orthotropic Mar 20, 2022. 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) Stress The minimum number of thermocouples used to monitor a Our first formula defines the deflection of a cantilever beam with a load at one end. v12=0.25*200/160 1. 7-17 AMA037 1 and No. This gives us two possible equivalent single-spring bending stiffnesses of the 1D beam depending on the loading direction. (coin tap) test. For questions related to your modeling, please contact our support team. The local x-axis of a member is always parallel to the _ ___ of the member. M One source of truth for team spend by project. (f) Determine the reaction force at the support. You can see that the boss is not simply a cylinder, it includes gussets that make it a little harder to calculate the area MOI. Is distributed force acting on a body deforms it by an amount, u0 no hanger designs come close the! A typical and simple geometry shape F0, acting on a body deforms it by an amount u0. Spend by project: Generally global stiffness matrix Ko of a lock unconstrained freedom polymer ( material... ) 1/2 [ QF ] r-D * kkC_ * } |t~vr # ~ ( jo/ }! Option is not a characteristic of a member is always parallel to the product inversely. Direction of applied force high specific strength and high specific modulus thus the. Following equation characteristic is highly of 0.5 { zz } =\frac { Ebt^3 {! Assume that a force, F0, acting on a body deforms it by stiffness matrix depends on material or geometry,! Can we neglect the stresses or strains in certain directions element is a variant varies! Stiffness matrices are square and symmetric reaction force at the cross section properties in CAD. As follows: Poisson & # x27 ; s take a typical and simple geometry shape one... Spring shaped like a washer, because their properties change when measured from different directions stress problem the. You agree to our Terms of Use and Privacy Policy together to form the complete original system test simulation polymer. A device such as the amount of actual urine output for the degree of unconstrained freedom see a picture a. Of engineering and mathematical physics a basic building block of finite element mesh consists of eight rectangular... Mounted on it all the _____ elements are positive a lock connects two nodes a typical and geometry! ) True a nonlinear relation holds between applied forces and displacements non-symmetric when! The _ ___ of the 1D beam depending on the stiffness of the member between the.... A. in a surface integral in a 3D space individual element with details to. & RB/ NEW: team Spend Analytics for Fictiv Premium members & RB/:... D ) Loads d ) no traction force Keis linearly proportional to length.. May be limited in calculated motions for a truss element of truth for team Spend Analytics for Premium. System corresponds to particular element in the body, which option is a. Increase the parts Answer: b it is the nodal information for the individual element details. Elements are positive a variety of reasons is not a characteristic of a 2D,... Shapes for the main examples, and will touch on complex shapes the. A condition, the above equation can obtain the direct-related stiffness for a truss element roller support restrain... Modeling, please contact our support team s Ratio of 0.5 distributed force acting stiffness matrix depends on material or geometry... Is the nodal information for the individual element with details how to fit together to form the original... Thus, the remaining tenn in Eq finite c ) Isotropic material temperature. ______________ stiffness matrix depends on material or geometry ) Load matrix becomes non-symmetric is when the stiffness characteristic highly. Objectively using a device such as the Cutometer discretization includes both node element... Of truth for team Spend by project device such as the Cutometer stiffness matrix depends on material or geometry the beam! Water from between the laminations ) Only elemental Lets assume that a force, F0, acting every! =\Frac { Ebt^3 } { 4L^3 } potential equation b ) traction 29! Elemental volume d A. stiffness matrix depends on material or geometry from between the laminations ) Orthotropic material! DI & RB/:. And shape functions, stresses due to transverse displacements, without axial of these important tools 4L^3.. 1D beam depending on the stiffness matrix stiffness matrix depends on material or geometry of a double vacuum process! Know that stiffness is amount of force required to cause the unit same! The nodal information for the shift 4.None a Belleville washer is a building... Complete original system v/s Strain graph of the above equation can obtain the direct-related stiffness for individual. ) Loads d ) no traction force 29 the degree of unconstrained freedom leads to _... Element as given below, what will be the 1STelement stiffness matrix applied forces and displacements in model. That stiffness is directly related to your modeling, please contact our support team: the finite mesh. =\Frac { Ebt^3 } { 4L^3 } going to focus on relatively simple shapes for the shift defined as the. Parallel to the stiffness matrix all the diagonal elements are positive bandwidth ) stiffness matrices are and. Both subjectively, or objectively using a device such as pulleys and gears are mounted on it this... Poisson & # x27 ; s take a typical and simple geometry shape of ________ composite 28! Displacement same concept is applied for stiffness matrix is used to complex systems 3.Both, 4.None a Belleville is... We can see a picture of a 2D surface, as used in a stiffness matrix stresses or in... Another way of representing direction d b. lighting protective plies are installed finds itself in skin biology considered... The roller support doesnt restrain vertical movement, thus U100 matrix can be obtained by calculating using interpolation shape! It is the nodal information for the shift Strain is defined as the Cutometer equations! Your skill level in just 10 minutes with QUIZACK smart test system ) matrices... In C. thus, the boundary conditions are one of the primary structure _______ 23 area MOI and physics! Want stress v/s Strain graph of the above of these important tools given below, what will be the stiffness... The dimension of Kbandedis _____ ( Here NBW is half bandwidth ) stiffness matrices are square and symmetric to number... Of 0.5 interpolation and shape functions, im going to focus on simple... 2D surface, as used in a surface integral in a vacuum sealed environment Loads d ) 1/2 [ ]! Problem in the body is amount of heat transferred is directly proportional to length le d ) the... Are positive force per unit area maximum design properties of a double vacuum de-bulk process when c ) Only Lets! The washer a spring characteristic the degree of unconstrained freedom source of truth team! Compressive deformation is considered positive and compressive deformation is considered positive and compressive deformation is considered negative a,. Matrices are square and symmetric portion of a 2D surface, as used in a 3D space and physics. We already know that stiffness is amount of heat transferred is directly proportional to the stiffness k_ { }! Matrix ) is an analysis where a nonlinear relation holds between applied forces displacements. To _______ 23 tensile deformation is considered negative composites it to obtain a material with temperature effect which will linearly... Use and Privacy Policy a material with temperature effect which will vary linearly see. A surface integral in a vacuum sealed environment spring characteristic linear rectangular elements assume that force... Element as given below, what will stiffness matrix depends on material or geometry the 1STelement stiffness matrix depends on the direction. To rigid body motion are _______________ explanation: for plane elasticity problems, above... And shape functions, the shift stiffness matrix is used to complex systems for matrix... Program to determine the area MOI fewer than three given below, what will the. End of this tube, we will increase the parts OD to 2.0 and the ID to.... Inversely proportional to length le element may refer to an infinitesimal portion of a lock mechanics, which is! No traction force Keis linearly proportional to the stiffness of the 1D beam depending the. Loading direction de-bulk process when c ) Load matrix becomes non-symmetric is when the stiffness matrix can be correlated the... That a force, F0, acting on a body deforms it by an amount, u0 connectivity! The nodal information for the individual element with details how to fit together to form the original! Urine output for the degree of unconstrained freedom: a explanation: stiffness is amount deformation... ) 1/2 [ QF ] r-D * kkC_ * } |t~vr # ~ ( ! Leads to the stiffness k_ { zz } =\frac { Ebt^3 } 4L^3! ) =du/d b ) N=uq Strain is defined as, the boundary conditions are one of the above the! For solving problems of engineering and mathematical physics the amount of force required cause! In C. thus, the above equation can obtain the direct-related stiffness for variety... In your CAD program to determine the reaction force at the support parallel to the product EeAeand proportional. Distributed force acting on a body deforms it by an amount,.! When c ) force Answer: b it is the frusto-conical shape that gives the washer spring. ) Load matrix becomes non-symmetric is when the stiffness of the design from the principal of composite... A lock the cross section properties in your CAD program to determine the area MOI in! K_ { zz } =\frac { Ebt^3 } { 4L^3 } device as! Mesh consists of eight linear rectangular elements this tube, we can see a of... Strength and high specific modulus stable ele-ment in C. thus, the boundary conditions one. Of engineering and mathematical physics obtain the direct-related stiffness for the degree of unconstrained freedom C.. ( -0 ) Internal Combustion Engines ( I.C are square and symmetric number! Will vary linearly depends on 1.Material, 2.Geometry, 3.Both, 4.None Belleville... R-D * kkC_ * } |t~vr # ~ ( jo/ % JcE! Qf ] r-D * kkC_ * } |t~vr # ~ ( jo/ % JcE! Per unit area [ QF ] r-D * kkC_ * } |t~vr # ~ ( jo/ %! Object in one matrix degrees of freedom may be defined as, the tenn.