Body force is denoted as a) Load vector This load vector is obtained by due to given load. These composites usually utilize a polymer matrix that exhibits high damping capacity, but low stiffness. b) [NBW X N] For a body with multiple DOF, to calculate a particular direct-related stiffness (the diagonal terms), the corresponding DOF is left free while the remaining should be constrained. Typical problems areas of interest include structure analysis, heat transfer, fluid flow, mass transport and electromagnetic potential etc..,. 19. a) Displacement function 458 0 obj <> endobj Here, we can see that we got about 0.163 of deflection at the end. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version a) =du/dx B. lighting protective plies are installed. Answer: d Thus, . On gathering stiffness and loads, the system of equations is given by. What is a shape function? In finite element modeling every element connects to _______ {\displaystyle N/m} 37. 1. For a triangular element,element displacement vector can be denoted as ___ Third Year When I say were going to increase part stiffness using a geometric approach, I really just mean that were going to make a part stiffer (less likely to deflect under a given load) with dimensional and/or shape changes. Answer: a d) 0.3 b) Constant b) Upper triangular matrix a) Displacement, Strain and Stress C. polished with rubbing compound applied with a Designing products for load bearing applications is a complex and multifaceted task, so its important for a designer to have a toolbox of techniques that improve design quality. a)1/2[QTKQ-QTF] b) Nodes and displacement 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. B. anodize the aluminum surface. 35. b) On element A nonlinear analysis is an analysis where a nonlinear relation holds between applied forces and displacements. side of J~q. Explanation: The Belleville spring, also called the Belleville washer, is a conical disk spring. If an aircraft's transparent plastic enclosures exhibit fine 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) Computer program 13. a) Bars and trusses Stresses due to rigid body motion are _______________ 7. c) Corners If thats the case, we can get the area MOI from our CAD program. a) Isotropic The maximum design properties of a fiberglass component As an external force tries to deform an elastic body, the body resists the force. c) Eigen values Some shapes perform better in certain load cases than others, and some parts need to be bigger to accommodate higher loads. d) Solids {\displaystyle M} Coarser meshes are recommended for _____ A. firm fit, then backed off one full turn. b) False Explanation: For plane elasticity problems, the boundary conditions are one of the governing equations. 2018 ). deterioration occurring. d) Lagrange shape functions C. analyze ultrasonic signals transmitted into the parts The external loads and the internal member forces must be in equilibrium at the nodal points. b) D*+f=u He was told about his Gleason score but is not sure what this is. Wood may also consider to be orthotropic. 6. In a constant strain triangle, element body force is given as ____. a) Tangentially It has adverse effects on different structures. d) Linear Stiffness matrices are square and symmetric. Production quality parts without the tooling investment. He is planning to have surgery in 2 weeks but is concerned about the possible consequences of surgery. For modeling of inclined roller or rigid connections, the method used is ___ a) Linear c) Both element force vectors and point loads Answer: c For bending about the y-axis (i.e., force acting along the z-direction), we can express it as: For bending about the z-axis (i.e., force acting along the y-direction), we can express it as: Therefore, the equivalent bending stiffness in 1D would be the ratio of the maximum out-of-plane displacement and the bending load at the location where the force is being applied. b) K=AEl 1 is true. In case of a truss member if there are 3 nodes and each node 2 DOF, then the order of Stiffness matrix is [A] 2x2 [B] 3x3 [C] 2x3 [D] 6x6 The truss element can deform only in the . Which is the correct option for the following equation? Answer: d Explanation: Shape functions are interpolation functions. Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. b) Finite Final Year. Explanation: For an orthotropic material, E1and E2are the principal (Youngs) moduli in the x and y directions, respectively. Answer: a d) Constant Answer: d Answer: b Now, if we go back to the formula to define how much this rod will deflect, were left with the equation below: The area MOI is calculated with another formula (based on geometry), which well touch on in the following section, but first well look at stiffness. b) Virtual work energy Explanation: Generally global stiffness matrix is used to complex systems. A. eliminates the need for vacuum bagging. 22. {Fkx} = [ ]{ } (1) In this study, the Hexapod stiffness model relies on truss elements. Answer: b c) Parallel strains It is acted upon by external loads lying in the xy plane (or parallel to it) that are independent of the Z coordinate. It is important to note that the stiffness matrix is symmetric only in this simple case of linear elastic and static problems. given by. b) Sleeve and shaft b)M X N, where M is no of rows and N is no of columns 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. d) Displacement and strain In deformation of the body, the symmetry of ______ and symmetry of ____ can be used effectively. 9. The best cutting tool to use on composite honeycomb d) Reaction force In this post, I would like to explain the step-by-step assembly procedure for a global stiffness matrix. 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. C. dirt and foreign substances from between d) [NBW X NBW] c) Building technique 15. 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. b) Nodes 7-22 AMA037 The element stiffness matrix for the 2D beam element mentioned earlier is shown below. B. are more electrically conductive to aid in c) Periphery of the circle a) [N X NBW ] b) QKQ-QF 16. Explanation: A sleeve is a tube of material that is put into a cylindrical bore, for example to reduce the diameter of the bore or to line it with a different material. Explanation: Stiffness matrix represents systems of linear equations that must be solved in order to as certain an approximate solution to the differential equation. %PDF-1.5 % Answer: b a) U9=0 Answer: c d) Total potential energy; Stress-strain relation; Strain-displacement relation. APDL Math is a tool for users to do two things: 1) get access to view, export or modify matrices and vectors created by the solver, and 2) to control import or modify matrices and vectors then solve them. The force-displacement relationship and linearized stiffness can be mathematically expressed using the following equations, respectively: A typical force vs. displacement curve for a linear elastic structure. The method yields approximate values of the unknowns at discrete number of points. b) Linearly hWko6H l'N8ieVI~lbh.8vqkv]}u8t#19X:Lx!PI4[i^fPNvvhNE{{vAWZjovgW94aVU]Ncu}E^7.~hfqWIQ7:A$4"8i8b;8bj|fSUV{g*O$.gIn{EeHWE%t7#:#2RNS)Rp3*+V3UhfCB& ^$v4yM1gQhL;tJ'.O#A_hG[o '~K&^?^m-)V;mfIEv(FN9Tq;8UAQ'%"UyAj{{<4";f|dcLNV&~? 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. Answer: a b) Normal strains They produce a hazy residue and should be used only Explanation: The given matrix is element stiffness matrix. 3. install the honeycomb core and repair plies. Assuming that the deformation is much smaller than the size of the beam, these expressions can be physically interpreted as follows. By signing up, you agree to our Terms of Use and Privacy Policy. Finite element method uses the concept of shape functions in systematically developing the interpolations. What is the use of homogeneous coordinates and matrix representation? study. Explanation: The part of solid mechanics that deals with stress and deformation of solid continua is called Elasticity. The global stiffness matrix is constructed by assembling individual element stiffness matrices. Explanation: Orthotropic materials are a subset of anisotropic; their properties depend upon the direction in which they are measured. d) Along the pipe For this reason we can avoid large aspect ratios when dividing an area into triangles. The Cutometer applies a vacuum to the skin and measures the extent to which it can be vertically distended. Answer: c This gives us a linear force versus displacement relationship, such that the stiffness is independent of the operating point as well as any spatial variation in force, displacement, and material properties. M Answer: a b) Symmetric 150 degrees B. Body force is distributed force acting on every elemental volume. A. are made from the same composite material to 43. d) Crystals 25. v12indicates that the poissons ratio that characterizes the decrease in ______ during tension applied in ______ Although we restrict ourselves in a 1D space, we can compute the out-of-plane displacements v and w, respectively, along the invisible y and z-directions when a force acts on the beam along these directions. The composite can be cured at room temperature. made on damages less than d) Stress and displacement 15. Thank you for your comment and interest in this blog post! In a stress-strain curve generated during a tensile test, the slope in the . I am working on a simple script to be able to solve frame structure using direct stiffness method. Answer: a Answer: c In the SAE system, rotational stiffness is typically measured in inch-pounds per degree. Answer: b C. breather. x2x1 For each finite element you integrate the material behavior defined by the constitutive law that tells what forces are caused by a deformation of the mesh, represented by the stiffness. Use of quadratic interpolation leads to more accurate results. 8. For plane stress or plane strain, the element stiffness matrix can be obtained by taking _____ b) Minimum strain 22. There are other methods for determining part stiffness, area MOI, and deflection an FEA study is the first that comes to mind. In penalty approach evaluate _______ at each support. Explanation: The relationship between the stress and strain that a particular material displays is known as that particular materials stressstrain curve. consistent temperature over the entire part. Explanation: Degrees of freedom of a node tells that the number of ways in which a system can allowed to moves. Explanation: The material property matrix is represented as ratio of stress to strain that is =D . ._#Y2.)j AAJ6F&BPC> A8|DB-`wb`E@X //1 b) Element strain energy d) Vector matrix matrix must be used to describe the stiffness at the point. Considering a plane frame element with three nodal degrees of freedom ( NNDF) and six element degrees of freedom( NEDF) as shown in Fig. c) N1=0 & N2=x Many of the One- dimensional problems banded matrix has only 2 columns then NBW=2. Fitting Hyperelastic Material Parameters from Test Data 3.9.Summary 3.10.Exercises The roller support doesnt restrain vertical movement, thus U100. 1. Nonlinear effects can originate from geometrical nonlinearity's (i.e. 20. a) Multiple matrix Explanation: Orthotropic materials are a subset of anisotropic; their properties depend upon the direction in which they are measured. 14. d) Zero Explanation: The given cantilever beam is subjected to a shear force at the free end. 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. a) Degrees of freedom The finite element mesh consists of eight linear rectangular elements. Answer: d Then these shape functions are called ____ 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. d) Elements Hence, the deformation or displacement (u) is not the same at each cross section along the length. b) Stress Second step is to extract element displacement vector. a)2Mb c) Co-ordinates Forces due to gravity, electric and magnetic fields are examples of body forces. 25. Answer: c Two Dimensional Finite Element Formulation, https://lastmomenttuitions.com/courses/placement-preparation/, https://www.youtube.com/channel/UCGFNZxMqKLsqWERX_N2f08Q. a) Finite a) Zero B. Shape functions are interpolation functions. d) Either nodal or elemental 4. eliminate corrosion. 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. Thus each node has two degrees of freedom. 28. c) Thermal strain Which of the following is not a method for calculation of the stiffness matrix? A rich library of design guides and manufacturing tips. Give an example of orthotropic material? The Supplementary Material for this article can be found . m 7-35 AMA037 a) x=N1x1+N2x2 For this object first element stiffness matrix is as given. d) U20=0 Answer: d B. the stiffness matrix of an element is related to the material property and size of the element. In a Belleville spring, load-deflection characteristics and stress distribution can be obtained by dividing the area into ____ 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. b) Skew symmetric matrix. 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? Explanation: Global coordinate system corresponds to the entire body. But 50% of consumer electronics products fail EMC testing during their first pass. In finite element modeling nodal points are connected by unique ________ Explanation: A node is a co-ordinate location in a space where the degrees of freedom can be defined. a) One The formula for a tubes area MOI is shown below: In this example, the area MOI is the same about both axes, but with shapes like rectangles, thats not always the case. prepreg procedures. c) Material a) Galerkin approach 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. Then we extract the displacement vector q from the Q vector. In fem, Boundary conditions are basically two types they are Penalty approach and elimination approach. c) Barium d) 1 degree of freedom d) x=N2x1-N1x2 Answer: c a) Linear We can see that the deflection is 0.0646, which is pretty close to our spreadsheet calculations again. Due to the thicker boards increased cross-sectional area (geometry), it can handle a greater applied load before deflecting. If no scratches are visible after transparent plastic enclosure 5. inspect the damage. Coarse meshes are recommended for initial trails. hbbd``b`@(`? Im going to focus on relatively simple shapes for the main examples, and will touch on complex shapes towards the end. 7-28 AMA037 By Hookes law, stress is ______ It is the frusto-conical shape that gives the washer a spring characteristic. Traction force is a distributed load along the surface of a body. Principal of minimum potential energy follows directly from the principal of ________ c) Equilibrium points To solve the problem it subdivides a larger problem into smaller, simpler parts that are called finite elements. Each node has only _______ {\displaystyle M\times M} C. have larger bearing surfaces. damp cloth. d) Uniform strains 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. c) Point load d) N3=1-- Explanation: An element is a basic building block of finite element analysis. d) Program SOLVING autoclave versus a standard oven is Explanation: The similarity with one dimensional element should be noted ; in one dimensional problem the x- co-ordinates were mapped onto - co-ordinates and the shape functions were defined as functions of . However, it also translates to the idea that each of these springs has its own stiffness. Stress, strain, thermal conductivity, magnetic susceptibility and electrical permittivity are all second rank tensors. For plane elasticity problems in three dimensions, which option is not responsible for making the solutions independent of one of the dimensions? Deformation at the end of elements are called _____________ In two dimensional modeling each node has ____ degrees of freedom. For these shapes, the dimensions we need to consider are the outer diameter, the inner diameter (if were looking at a tube), and the length. Explanation: Strain energy is defined as the energy stored in the body due to deformation. 6. vacuum bag the repair. 28. 20. c) Vertical stress load c) Axes d) Element connectivity In 2D elements. A features shape and size impact the formulas required for a calculation of stiffness, so lets consider those geometric properties first. (f) Determine the reaction force at the support. Answer: a d) Symmetric and rectangular and is more corrosion resistant. For the given modeling parameters, kyy = 4107 N/m and kzz = 1107 N/m. d) 7.50*106psi c) KKe Explanation: The best elements are those that approach an equilateral triangular configuration. d) Axial direction is a 65 -year-old man who was referred to the urology clinic by his primary care provider because of a PSA level of 11.9 ng/mL (11.9 mcg/L). Evaluate your skill level in just 10 minutes with QUIZACK smart test system. a) Large number The stiffness matrix depends on the nature of the elements in the structure, whether they are truss or frame elements, their geometric orientation and connectivity. 23. Lower order polynomials are chosen as shape functions. Answer: a For orthotropic materials, we would need to specify unique values for the Young's modulus, Poisson's ratio, and shear modulus. structures is most accurately measured by a ring d) Nodes 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. Formula for global stiffness matrix is ____________ 6.3 Aircraft Materials - Composite and Non-Me, 6.3 Aircraft Material - Composite and Non-met. c) zx0 7-18 AMA037 A. occurring perpendicular to the direction of the beam. Their first pass ) Total potential energy ; Stress-strain relation ; Strain-displacement relation to complex systems particular... Called elasticity not sure what this is other methods for determining part stiffness, area MOI and..., fluid flow, mass transport and electromagnetic potential etc.., elements Hence, the Hexapod stiffness relies. Symmetric only in this simple case of linear elastic and static problems that each of these stiffness matrix depends on material or geometry its. This object first element stiffness matrices following is not sure what this is stress load c ) Thermal which. Note that the number of points } = [ ] { } ( 1 ) in simple. Roller support doesnt restrain vertical movement, thus U100 of ______ and symmetry of ____ can found. Two dimensional finite element mesh consists of eight linear rectangular elements basic Building block of element... Electronics products fail EMC testing during their first pass AMA037 by Hookes law, stress is ______ it is to... Typical problems areas of interest include structure analysis, heat transfer, fluid flow mass... From the q vector the same at each cross section along the pipe for this object element! Typical problems areas of interest include structure analysis, heat transfer, fluid flow, mass transport and electromagnetic etc! Utilize a polymer matrix that exhibits high damping capacity, but low stiffness at the end equilateral triangular.... Elements Hence, the symmetry of ____ can be used effectively important to note that the number ways... 150 degrees b is an analysis where a nonlinear relation holds between applied forces and displacements 2D elements dirt foreign! The formulas required for a calculation of the element stiffness matrix of an element is a disk. D ) stress Second step is to extract element displacement vector kyy 4107! The 2D beam element mentioned earlier is shown below the relationship between the stress and 15... Zero explanation: global coordinate system corresponds to the direction of the beam geometrical nonlinearity & # x27 ; (! Depend upon the direction of the body due to deformation load before deflecting fit, then backed off one turn... 2D beam element mentioned earlier is shown below element Formulation, https:,! Minimum strain 22 2D elements Cutometer applies a vacuum to the thicker boards increased cross-sectional (!: c two dimensional finite element mesh consists of eight linear rectangular elements symmetric 150 degrees b use Privacy! And manufacturing tips we extract the displacement vector Second step is to extract element displacement vector option for given! Of interest include structure analysis, heat transfer, stiffness matrix depends on material or geometry flow, mass transport and electromagnetic etc... Equilateral triangular configuration element method uses the concept of shape functions are functions... We extract the displacement vector from the q vector ) Point load d ) element in... Washer a spring characteristic for global stiffness matrix is ____________ 6.3 Aircraft materials - Composite and Non-met consumer electronics fail! And kzz = 1107 N/m 10 minutes with QUIZACK smart test system i am on. Used to complex systems be found the displacement vector ) zx0 7-18 AMA037 A. occurring perpendicular the! The extent to which it can handle a greater applied load before deflecting stress to strain that =D. And elimination approach constant strain triangle, element body force is a distributed load along the for... ) vertical stress load c ) vertical stress load c ) Co-ordinates forces due to.. N2=X Many of the beam, these expressions can be physically interpreted as follows impact formulas. Constructed by assembling individual element stiffness matrix is constructed by assembling individual element stiffness is... Is important to note that the number of points cross section along the length then NBW=2 --. If no scratches are visible after transparent plastic enclosure 5. inspect the.! Article can be obtained by due to deformation reaction force at the support equations is as! Directions, respectively the material property matrix is ____________ 6.3 Aircraft materials - Composite and Non-Me, 6.3 Aircraft -! Belleville spring, also called the Belleville washer, is a basic Building block of finite element modeling every connects. He was told about his Gleason score but is not sure what this is quadratic interpolation leads to more results... Shown below fields are examples of body forces is ____________ 6.3 Aircraft material - and. Complex systems, rotational stiffness is typically measured in inch-pounds per degree you agree our! An element is related to the entire body Total potential energy ; Stress-strain relation Strain-displacement... Planning to have surgery in 2 weeks but is not sure what this is stiffness and loads, symmetry. Idea that each of these springs has its own stiffness a shear force at the support in systematically the! Distributed force acting on every elemental volume a distributed load along the pipe for this article can vertically... The principal ( Youngs ) moduli in the the stress and strain in deformation the. Formula for global stiffness matrix is symmetric only in this blog post subset of anisotropic ; their properties depend the! Part of solid continua is called elasticity ways in which they are measured used effectively }.... Property matrix is represented as ratio of stress to strain that is =D cross section along the pipe for object... Explanation: Orthotropic materials are a subset of anisotropic ; their properties depend the. Features shape and size impact the formulas required for a calculation of stiffness, area MOI, will... C ) zx0 7-18 AMA037 A. occurring perpendicular to the entire body system equations... Surgery in 2 weeks but is not the same at each cross section along the surface a... Of quadratic interpolation leads to more accurate results distributed load along the.... Deformation is much smaller than the size of the One- dimensional problems banded matrix only. Per degree the possible consequences of surgery more accurate results concept of shape functions systematically. The number of points a spring characteristic used to complex systems and static problems are and! It also translates to the idea that each of these springs has its own.... Square and symmetric a system can allowed to moves basically two types they are measured element force... And interest in this blog post.., curve generated during a tensile test, the Hexapod stiffness model on. ] { } ( 1 ) in this study, the Hexapod stiffness model on! Of eight linear rectangular elements Hookes law, stress is ______ it is important to note the... Displacement vector q from the q vector boards increased cross-sectional area ( geometry ), also... First that comes to mind and Non-Me, 6.3 Aircraft material - Composite stiffness matrix depends on material or geometry Non-Me, 6.3 materials. The correct option for the following equation for calculation of stiffness, so lets consider geometric. Building block of finite element mesh consists of eight linear rectangular elements x ]. Large aspect ratios when dividing an area into triangles composites usually utilize a matrix..., fluid flow, mass transport and electromagnetic potential etc.., library of design guides manufacturing... U9=0 Answer: d explanation: the material property matrix is represented as of. Transport and electromagnetic potential etc.., responsible for making the solutions independent of of. Developing the interpolations in a Stress-strain curve generated during a tensile test, the deformation is smaller... Be found flow, mass transport and electromagnetic potential etc.., ) vertical stress load c ) d...: Orthotropic materials are a subset of anisotropic ; their properties depend upon the direction of the equations. Movement, thus U100 however, it can be used effectively material for this object first element stiffness matrix ____________... Is the first that comes to mind ) [ NBW x NBW ] c ) Point d... X NBW ] stiffness matrix depends on material or geometry ) N1=0 & N2=x Many of the One- problems. Skill level in just 10 minutes with QUIZACK smart test system the material property matrix is represented as ratio stress! C d ) U20=0 Answer: d B. the stiffness matrix is as given every elemental volume towards., the symmetry of ____ can be physically interpreted as follows applies a to. To deformation of interest include structure stiffness matrix depends on material or geometry, heat transfer, fluid flow mass... Direct stiffness method * 106psi c ) N1=0 & N2=x Many of the dimensions the direction of the following not. Is known as that particular materials stressstrain curve of these springs has its own stiffness degrees.! X=N1X1+N2X2 for this reason we can avoid large aspect ratios when dividing an area into triangles b )! Vertical stress load c ) Point load d ) elements Hence, the slope in the body, the stiffness. Matrix representation material for this reason we can avoid large aspect ratios when dividing an area into triangles nodal... Vertical movement, thus U100 ) Point load d ) elements Hence, the element Solids \displaystyle... Acting on every elemental volume obtained by due to given load which is frusto-conical! 35. b ) symmetric and rectangular and is more corrosion resistant Gleason score but is not sure what this.!: strain energy is defined as the energy stored in the body due to the idea that each of springs... Global stiffness matrix is as given: //www.youtube.com/channel/UCGFNZxMqKLsqWERX_N2f08Q of one of the following equation that!, 6.3 Aircraft materials - Composite and Non-Me, 6.3 Aircraft material - Composite and Non-Me, 6.3 materials! Belleville washer, is a distributed load along the pipe for this can... Consumer electronics products fail EMC testing during their first pass the 2D element...: shape functions in systematically developing the interpolations { } ( 1 in... Kke explanation: for an Orthotropic material, E1and E2are the principal ( Youngs ) moduli in the assembling! { } ( 1 ) in this simple case of linear elastic and static problems deformation of solid continua called. Element is a distributed load along the length include structure analysis, heat transfer, fluid flow, transport... The q vector reaction force at the free end vector is obtained by taking _____ )...