Explanation: Natural coordinate system is another way of representing direction. Explanation: Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. a) Programming equations Finite element method uses the concept of _____ =EBq. The shape functions are physically represented by area co-ordinates. Which is not an advantage of dry fiber composite procedures? When the stresses are determined in an orthotropic material, then they are used to determine ____ 2 are true. Explanation: Any linear combination of these shape functions also represents a plane surface. c) q=[q1,q2,q6]T a) Essential boundary condition 10. 25. Note that based on the chosen boundary conditions (clamped-free beam), the displacement components v and w would vary as a function of the x-coordinate. B. air from between the laminations. B. i am doing uniaxial compression test simulation of polymer (ABS material ). A. pick up the "noise" of corrosion or other 29. Answer: a Think of two cantilever beams one made of steel and the other plastic both with identical dimensions. u= N1u1(e)+N2u2(e). Answer: b Lower order polynomials are chosen as shape functions. I have a question. This can be evaluated both subjectively, or objectively using a device such as the Cutometer. 5, 2, 1, 4, 3, 6 Im going to focus on relatively simple shapes for the main examples, and will touch on complex shapes towards the end. b) Precision and accuracy Answer: b d) Geometry and loading B. material such as titanium or corrosion resistant steel. Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. 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. Metal fasteners used with carbon/graphite composite with transparent plastics? 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 plastic oversize by 1/8-inch. 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: a c) Galerkin approach If we require a small force, F, to deform the body by an infinitesimally small amount, u, then the ratio of these two quantities would give us the stiffness of the body at the operating point denoted by the state variables F0 and u0. a) True Answer: d Learn more about Fictivs solutions for large enterprise companies and schedule a consultation. b) Point loads only The points at where kinetic energy increases dramatically then those points are called _______ This is especially true if you dont use them on a regular basis, so Ill go over the process to clarify the math. Answer: d Here, we will show you how to use the Beam interface in the 3D space dimension to compute both the axial and the bending stiffness. 1. a) X direction Answer: d d) D*+f=u Answer: b 23. 7. Explanation: The loading on an element includes body force; traction force & point load. a) [N X NBW ] 7-20 AMA037 Chest x-ray, bone scan, and abdominal CT scan are all negative. 23. Answer: b Explanation: The given cantilever beam is subjected to a shear force at the free end. Today, stiffness usually refers to the finite element stiffness matrix, which can include all of the above stiffness terms plus general solid or shell . The first derivative of the out-of-plane displacement with respect to the x-coordinate represents the slope; the second derivative represents the curvature; and the third derivative is proportional to the shear force. When the applied force is released, the system returns to its original shape. function [stiffness_matrix] = global_stiffnesss_matrix (node_xy,elements,E,A) - to calculate the global stiffness matrix. c)1/2[KQ-QF] An Average Coupling Operator is used to evaluate the displacements at the point x = L. The with() operator is used to fetch the solution from the different load cases that the model is solved for. 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. squeezes resin more deeply into the structure. B. separation of the laminates. Now, to increase the parts stiffness, we will increase the parts OD to 2.0 and the ID to 1.5. The information of array of size and number of elements and nodes per element can be seen in ___ A laminate is a tough material that is made by sticking together two or more layers of a particular substance. 3. d) Boundary conditions a) Spherical A rigid body is usually considered as a continuous distribution of mass. c) Shape functions d) Nodes a) =du/dx c) 1- direction and 2- direction 7-21 AMA037 b) Plates and beams The principle advantage to curing composite parts with an Explanation: According to minimum potential energy theorem, that equilibrium configurations make the total potential energy assumed to be a minimum value. The points where triangular elements meet are called ____ Explanation: NBW means half bandwidth. The shape functions are physically represented by _____ State whether the above statement is true or false a) true b) false View Answer 2. A Fat boundary-type method for localized . 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. If the setup is Displacement-Controlled: b) Large deformations in linear elastic solids Press fit of a ring of length L and internal radius rjonto a rigid shaft of radius r1+ is considered. b) Finite a) Stiffness matrix B.19. a) A1/A d) Horizontal axis. a) Non symmetric and square 22. self-locking nuts, the nuts should be tightened to a b) Energy matrix flowing when reheated is described as Explanation: The constant strain triangle or cst 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. When an orthotropic plate is loaded parallel to its material axes, it results only _____ matrix becomes non-symmetric is when the stiffness characteristic is highly. a) uTTl 14. Example for plane stress problem is Strip footing resting on soil mass a thin plate loaded in a plane a long cylinder a gravity dam Show Answer 3. Hi, thank you for writing this blog. Explanation: Penalty approach is one of the method to derive boundary conditions of an element or a structure. 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. 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. In solid mechanics, what is the correct vector form of the equations of motion for a plane elasticity problem? Then elemental volume is given by b) The initial displacement only View Answer 3. b) Nodes C. low speed and low pressure drills. d) Banded matrix Answer: d a) Galerkin approach c) 7 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. Another application of stiffness finds itself in skin biology. Explanation: Deformation changes in an objects shape or form due to the application of a force or forces. c) Radially What is the actual equation of stiffness matrix? B. low speed and high pressure drills. B. allows curing in higher temperatures and pressures. Fictiv is your operating system for custom manufacturing that makes part procurement faster, easier, and more efficient. While part stiffness can be modified with geometry, material stiffness is a property of the material itself. For a plane strain problem, which strain value is correct if the problem is characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0? Explanation: The best elements are those that approach an equilateral triangular configuration. Modeling of a cylinder of infinite length subjected to external pressure. c) Non symmetric c) Linear b) Non uniform For time-dependent problems in FEA, which variables must be specified for each component of the displacement field problems? Where the members are organized so that the assemblage as a whole behaves as a single object. a) Load a) xx=0 d) Cannot be determined b) KeKe The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. In elimination approach method, extract the displacement vector q from the Q vector. Explanation: For plane elasticity problems, the equations of motion are one of the governing equations. The same element stiffness matrix can be obtained by calculating using interpolation and shape functions,. Nonlinear effects can originate from geometrical nonlinearity's (i.e. c) D2*+f=u Part One focuses on changing the geometry of structures to increase stiffness. hi 36. B. anodize the aluminum surface. For example, in Design Example 16.1, we discuss how a tubular shaft is designed that meets specified stiffness requirements. 7-38 AMA078 A second rank tensor looks like a typical square matrix. b) dV=dA 21. curing process. 3. a) Longitudinal axis. the same stiffness matrix obtainable from Ref. matrix must be used to describe the stiffness at the point. (f) Determine the reaction force at the support. 12. A. less than full strength curing of the matrix. d) Axial direction Use of linear shape functions results in a constant B matrix. b) Only nodal core material with thermoplastic resin. McqMate.com is an educational platform, Which is developed BY STUDENTS, FOR STUDENTS, The only structures must be constructed of A. thermoset. The points where the corners of the triangles meet are called nodes. In a constant strain triangle, element body force is given as ____. c) zx=0 a) Kinetic energy Fiber-reinforced composites are composed of axial particulates embedded in a matrix material. 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). c) f=[fx,fy]T This paper presents an investigation on the stiffness and energy absorption capabilities of three proposed biomimetic structures based on the internal architecture of a cornstalk. Next, we can solve the same model using the Timoshenko beam theory. EXTC Engineering Beams represent structures in which the cross-section is assumed to be small compared to the length. 7-44 AMA004 In these equations, we have used the displacement (w) along the z-direction for representational purposes. Explanation: The shape functions are physically represented by area co-ordinates. As shown here, you can create a switch using the if() operator and the names (such as root.group.lg1) associated with the Load Groups, such that only one component of the force vector can be made nonzero at a time when you are solving the same model for several load cases. c) Nodes and elements a) =D(-0) The roller support doesnt restrain vertical movement, thus U100. 7-14 AMA037 d) Surface co-ordinates b) =du/d Third Year Explanation: The stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. The force and displacement along the z-direction can be correlated using the stiffness k_{zz}=\frac{Ebt^3}{4L^3}. The round tube is almost as stiff as the solid round bar, even though the center is hollowed out. Crack propagation problems come under this category. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as. i want stress v/s strain graph of the above . C. Both No. He has a history of hypertension and atrial fibrillation, for which he receives warfarin (Coumadin), metoprolol (Toprol), digoxin, and lisinopril/hydrochlorothiazide (Zestoretic). having an order of, The determinant of an element stiffness matrix is always. Here is the workflow for obtaining the stiffness from the 1D model: A snapshot of the 1D model made using the Beam interface. composite fasteners c) N1=0 & N2=x Again, this is very close to our 170% difference in the spreadsheet calculations. The proper sequence of procedures to repair a damaged c) Displacement Write the element stiffness for a truss element. b) A-A1 c) Penalty approach Explanation: An example of a plane stress problem is provided by a plate in the XYZ Cartesian system that is thin along the Z-axis. included tip angle of is recommended. Explanation: Local coordinate system corresponds to particular element in the body. For CST shape functions are linear over the elements. In many one-dimensional problems, the banded matrix has only two columns. Answer: c a) Zero From where does the global load vector F is assembled? By signing up, you agree to our Terms of Use and Privacy Policy. A steel sleeve inserted into a rigid insulated wall. Explanation: Global coordinate system corresponds to the entire body. d) Two b) Load Unidirectional composites are stacked at different fiber orientations to form a ______ around edges or under fairings. Thus, xx0, yy0, zz0, xy0, where as yz=0 and zx=0. c) Force vector The external loads and the internal member forces must be in equilibrium at the nodal points. A. B. 9. 21. Answer: c . Strain is defined as the amount of deformation in the direction of applied force. Copyright 2021 Quizack . 4. applying pressure. a) u=Nq Second step is to extract element displacement vector. d) Lagrange shape functions b) Quadratical 2. Answer: b On the material side, stiffness depends on the modulus of elasticity, also known as Young's Modulus and abbreviated as E. Young's Modulus is the ratio of stress to strain at very small strains. Answer: b C. in proximity to fuel and other liquid. materials have been cleaned, their surfaces should be A snapshot of the Study settings illustrating how the load cases are set up to activate only one component of the force vector at a time. a) Displacement, Strain and Stress The principal material axes that are normal to the _______ Only No. The first step is adding a large number C to the diagonal elements of the stiffness matrix. b) Low traction force Answer: a Can we neglect the stresses or strains in certain directions. A. high speed, low pressure drills. throughout their Academic career. Screenshot of the Parameters table in the COMSOL software. 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. d) 0.3 In stiffness matrix, all the _____ elements are positive. Accelerate development with instant quotes, expert DFM, and automated production updates. Material Properties Check the entered material properties to make sure they are acceptable. Shape functions are interpolation functions. Even the simplest designs can be sensitive to part stiffness. c) Area co-ordinates The global stiffness matrix is constructed by assembling individual element stiffness matrices. b) Strain-displacement relation Explanation: The two dimensional region is divided into straight sided triangles, which shows as typical triangulation. v12=v21 E1/E2. d) Solids 23. Under such a condition, the above equation can obtain the direct-related stiffness for the degree of unconstrained freedom. b) =EB Explanation: The relationship is that connects the displacement fields with the strain is called strain displacement relationship. a) q=[q1,q2,q3]T At the given condition the shape functions are named as Lagrange shape functions. 1. Answer: d Explanation: The total potential energy of an elastic body is defined as sum of total strain energy and the work potential energy. d) Uniform stiffness matrix a) Laminate 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 :. b) Potential energy Second Year The _____ can be obtained even with coarser meshes by plotting and extrapolating. Is stiffness the same as elasticity matrix? d) Small deformations in non-Hookean solids d) Sleeve and couple What was the amount of actual urine output for the shift? In doing so, we get the following area MOI. First Year c) Circularly These composites usually utilize a polymer matrix that exhibits high damping capacity, but low stiffness. %PDF-1.5 % Answer: b The unknown displacement field was interpolated by linear shape functions within each element. In shape functions, first derivatives must be _______ within an element. A Belleville washer is a type of spring shaped like a washer. 2. Answer: b Principal stresses and their directions are calculated by using ____ b) Normal strains k Keep production lines running without the excess inventory. , Isoparametric formula is ______________ Answer: b if the stress of the element is below the yield stress, the stiffness is constant and doesn't change . c) Lower triangular matrix For a straight beam with a rectangular The inverse of stiffness is flexibility or compliance, typically measured in units of metres per newton. 43. be installed hot and tightened to a firm fit before the d) Linear The approach shown here for evaluating the stiffness components is applicable as long as we do not expect any coupling between extension and bending, (i.e., when the stiffness matrix is diagonal). [4] The pliability of skin is a parameter of interest that represents its firmness and extensibility, encompassing characteristics such as elasticity, stiffness, and adherence. d) Load vector These materials have three mutually perpendicular planes. 4. They are a subset of anisotropic materials, because their properties change when measured from different directions. 6.3 Aircraft Materials - Composite and Non-Me, 6.3 Aircraft Material - Composite and Non-met. As I mentioned previously, all shapes will have a different formula for area MOI. It is denoted by symbol . This further reduces the number of material constants to 21. Explanation: Shape functions are interpolation functions. 15. Let's take a typical and simple geometry shape. (i.e. The structural stiffness, maximum stress, densification strain, and . b) Degrees of freedom Explanation: Global load vector is assembly of all local load vectors. c) Elements FEM basis is in the stiffness matrix method for structural analysis where each element has a stiffness associated with it. Element stiffness is obtained with respect to its axes. Designing for part stiffness through geometric controls is one of these important tools. Explanation: For an orthotropic material, E1and E2are the principal (Youngs) moduli in the x and y directions, respectively. pressure system to absorb excess resin during curing called? d) =EBq B. bleeder. nonlocal or when the nonlocal effects become significant at a reduced scale of. c) Diagonal a) Stiffness matrix 38. Answer: c Explanation: By penalty approach we can derive boundary conditions of an element or a structure. 7-37 AMA078 The matrix representation for translation in homogeneous coordinates is, The matrix representation for scaling in homogeneous coordinates is, The two-dimensional rotation equation in the matrix form is. Production quality parts without the tooling investment. The finite element mesh consists of eight linear rectangular elements. d) Loads Which is the correct option for the following equation? d) Radius b) xz=0 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. There was 1175mL1175 \mathrm{~mL}1175mL left in the bag 8 hours. high strength and high elastic modulus for its weight.) plastic cools. Answer: a Answer: c The prostate is slightly tender on examination. The most frequent cause of damage to composite parts are b) Co-efficient of linear expansion 7-30 AMA037 11. of nodes 8. consistent temperature over the entire part. A.B. radiography are most effective finding defects Thus, xx, xyand yyare non-zero stresses. For a Belleville spring the load is applied on _____ Answer: d A zero rank tensor is a scalar, a first rank tensor is a vector; a one-dimensional array of numbers. Coarser meshes are recommended for _____ The COMSOL software also allows you to use the Timoshenko beam theory, which would be more appropriate for the accurate 1D modeling of low aspect ratio structures. b) yx0 d) Parabolic 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. Explanation: Strain is defined as a geometrical measure of deformation representing the relative displacement between particles in a material body. 1 and No. What is the material layer used within the vacuum bag What is meant by stiffness matrix? Body force is denoted as 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. The pistons run directly in the bores without using cast iron sleeves. a) True When symmetry is assumed about the mid plane, this plane is restrained in the _____ 7-34 AMA037 For general user elements all material behavior must be defined in subroutine UEL, based on user-defined material constants and on solution-dependent state variables associated with the element and calculated in subroutine UEL. Answer: c No hanger designs come close to the materials yield strength, but their function depends on the stiffness of the design. What is the use of homogeneous coordinates and matrix representation? b) Load 30. Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. Health problems resulting from composite repair processes The symmetry of stiffness matrix proves Explanation: The shape function is a function which interpolates the solution between discrete values obtained at the mesh nodes. Answer: d applied forces. 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. B. d) Three degrees of freedom Coarse mesh is more accurate in getting values. In the penalty approach, rigid support is considered as a spring having stiffness. Next, well solve for both stiffness and deflection, just to demonstrate how they correlate (if the derivation hasnt sold you already). In penalty approach, rigid support is considered as a spring having stiffness. 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). We know that a) Multiple matrix The terms in the matrix depend on the beam geometry and material - A is the area of the beam cross-section, E is the Young's modulus of the beam material, I is the second moment of area of the beam cross-section and L is the length of the beam element. lightning dissipation. 20. Is there any spatial inhomogeneity in the applied force? b) Natural boundary condition b) Upper triangular matrix b) = a) =D Explanation: From nodal displacement equation we can write that isoparametric equation as b) Curved By rigid body deformation is neglected so stresses are not considered. a) Rayleigh method b) False b) 90-180 Answer: d and is more corrosion resistant. The smaller elements will better represent the distribution. d) Kinematic energy Answer: b Explanation: A body force is a force which acts through the volume of the body. a) Linear A 1D representation of the beam, obtained using the balance of bending moment in the body. Answer: d Explanation: Boundary condition means a condition which a quantity that varies through out a given space or enclosure must be fulfill at every point on the boundary of that space. Explanation: A Belleville washer, also known as a coned-disc spring, [1] conical spring washer, [2] disc spring, Belleville spring or cupped spring washer, is a conical shell which can be loaded along its axis either statically or dynamically. . The load is applied on the periphery of the circle and supported at the bottom. His symptoms included nocturia times two and a history of erectile dysfunction. d) 4 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? , It is used to define nodes in the entire body. 7. 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. One dimensional element is the linesegment which is used to model bars and trusses. 40:60 5. 33. a) Tangentially A. high strength aluminum-lithium alloy. From solid mechanics, which traction(t) boundary condition is not correct for the following beam of thickness h? A.B. Explanation: A shaft is a rotating machine element, usually circular in cross section, which is used to transmit power from one part to another, or from a machine which produces power to a machine which absorbs power. d) 2- direction and 4- direction In the FEA of a fluid mechanics problem, we need to find . For example, for an element in tension or compression, the axial stiffness is, Similarly, the torsional stiffness of a straight section is. Explanation: In finite element modeling, each element connects to 2 nodes.
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