d) Elements d) T b) Finite Explanation: A stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. d) Assembling The principal material axes that are normal to the _______ The geometry of such test specimens has been standardized. 483 0 obj
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3. Such cases will be discussed in a future blog post. b) Modified stiffness matrix a) One of elements Explanation: According to minimum potential energy theorem, that equilibrium configurations make the total potential energy assumed to be a minimum value. From solid mechanics, which traction(t) boundary condition is not correct for the following beam of thickness h? This allows us to get more detailed information on spatial variation in displacement, stresses, and strains in the beam. consistent temperature over the entire part. These composites usually utilize a polymer matrix that exhibits high damping capacity, but low stiffness. Before we dive in, we need to define stiffness mathematically. a) Potential energy Answer: c The stiffness matrix is a inherent property of a structure. 2. d) Crystals Answer: b u= N1u1(e)+N2u2(e). This can be evaluated both subjectively, or objectively using a device such as the Cutometer. Stiffness matrix depends on (A) material (B) geometry (C) both material and geometry (D) none of the above Answer C QUESTION No - 16 Example of 2-D Element is ___________ . B. The most general anisotropic linear elastic material therefore has 21 material constants. Each node is subjected to two degrees of freedom (figure 3a) and 2 nodal forces (figure 3b). b) Skew symmetric matrix. deterioration occurring. In temperature effect, initial strain, 0= ____ c) N3=1- d) Both penalty approach and elimination approach c) U10=0 Assuming that the deformation is much smaller than the size of the beam, these expressions can be physically interpreted as follows. c) Global stiffness matrix c) Singular stiffness matrix d) Element The Constant strain triangle can give____ stresses on elements.
b) Potential energy A 0D representation of the beam using a lumped stiffness, k, with a force, F, acting on it that produces a displacement, u. In stiffness matrix nodal displacements are treated as basic unknowns for the solution of indeterminate structures. c)Mb 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. 18. d) Infinite no of nodes b) Direct stiffness matrix objective of our platform is to assist fellow students in preparing for exams and in their Studies c) Polynomial B. low speed and high pressure drills. Which is true regarding the use of polymerizable cements c) Strain along any one direction is zero a) K={k}e For a circular pipe under internal or external pressure, by symmetry all points move _____ a) Co-efficient of thermal expansion a) Isotropic This means that we need to decide whether the structure is a single spring or a network of springs distributed in space and connected to each other.
ultrasonic monitoring The stiffness of the spring is defined as, (2) Explanation: A global stiffness matrix is a method that makes use of members stiffness relation for computing member forces and displacements in structures. Axisymmetry implies that points lying on the z- axis remains _____ fixed. a) x=N1x1+N2x2 Explanation: 8. A1is the first area and N1is its shape function then shape function N1= ___ 11. Answer: b 5. inspect the damage. N1=A1/A . {\displaystyle M\times M} Answer: b What is a shape function? For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. C. allows circulation of the heated air for a more 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. d) 44 The skin maintains its structure due to its intrinsic tension, contributed to by collagen, an extracellular protein that accounts for approximately 75% of its dry weight. 7. By using ___ 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 material's stiffness indicates its ability to return to its original shape or form after an applied load is removed. Using a simplistic definition where stress is equal to force per unit cross-section area, \sigma=F/A, where A=bt, and strain is equal to the ratio of deformation to the original length, \epsilon=u/L, and combining these, we get F=(EA/L)u. Explanation: To calculate the magnitude, assume that the force causing the moment is linear with y. When symmetry is assumed about the mid plane, this plane is restrained in the _____ The performance of finite element computation depends strongly on the quality of the geometric mesh and . A. high strength aluminum-lithium alloy. 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. Explanation: Hookes law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid. Explanation: Natural coordinate system is another way of representing direction. By signing up, you agree to our Terms of Use and Privacy Policy. c) Diagonal If we need the stiffness to be about the same, we dont have to add much to the outer diameter. Explanation: Global load vector is assembling of all local load variables. 16. How many nodes are there in a hexahedron element? d) xz0 Hi, thank you for writing this blog. c) Both Precision and accuracy c) B=q c) Galerkin approach That is all. Answer: a 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. A. covered with a thin coat of wax. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as. b) Multiple constraints Hence, we can express the axial stiffness of the beam for this 0D model with the following equation: Assuming the Youngs modulus of steel is 200 GPa, we find that the axial stiffness of the beam is k = 4109 N/m. Answer: a 7-33 AMA037 c) Displacement 7-18 AMA037 a) Bars and trusses A. assembled with certain aluminum alloys. 7-22 AMA037 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? c) Total potential energy At the end of the shift, 2535mL2535 \mathrm{~mL}2535mL were emptied from the drainage bag of the irrigation system. c) x=d/du Forces due to gravity, electric and magnetic fields are examples of body forces. Materials have a long shelf life. Answer: b A crack formed as a result of Thermal stress produced by rapid cooling from a high temperature. An example of this is provided later.) A. Element connectivity is the nodal information for the individual element with details how to fit together to form the complete original system. Fictiv is your operating system for custom manufacturing that makes part procurement faster, easier, and more efficient. b) Thermo couple d) No. The differences may be a result of the deflection spreadsheet approximating the interaction at the base, as well as small calculation margins combined between the FEA (which likely uses a more complex 3D stiffness matrix approach) and generalized deflection equation. =0.3125. b) Notches and fillets 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. b) Two B. the ability of the fibers to transfer stress to the matrix. 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. Try a value of 0.48 instead. Explanation: The given matrix is element stiffness matrix. heat cycle is We can write the stress-strain relations for a linear elastic material exploiting these symmetries as follows: 2 6 6 6 6 6 6 4 11 22 33 23 13 12 3 7 7 7 7 7 7 5 = 2 6 6 6 6 6 6 . The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or different points) or the same degree of freedom at two different points. A Fat boundary-type method for localized . Explanation: Elasticity is the part of solid mechanics that deals with stress and deformation of solid continua. For questions related to your modeling, please contact our support team. Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. Answer: c c) Z direction d) 1 degree of freedom A. less than full strength curing of the matrix. d) Co-ordinate c) Thermal expansion A Global Evaluation is used to print the values of kxx, kyy, and kzz. 7. Lets assume that a force, F0, acting on a body deforms it by an amount, u0. Answer: b b) Spherically a) f=[fx,fy]T C. install anchor tabs on the aluminum surface. Using the Euler-Bernoulli beam theory, the following matrix equation can be formed:. Answer: a a) q=[q1,q2,q3]T Another application of stiffness finds itself in skin biology. 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. Unidirectional composites are stacked at different fiber orientations to form a ______ a) Longitudinal axis. A rigid body is usually considered as a continuous distribution of mass. Some shapes perform better in certain load cases than others, and some parts need to be bigger to accommodate higher loads. 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 . geometry/distribution, and properties of the con-stituent phases, it is possible to design materials with property combinations that are better than those found in the metal alloys, ceramics, and polymeric materials. Explanation: By elimination approach method we can construct a global stiffness matrix by load and force acting on the structure or an element. The element stiffness matrix for the 2D beam element mentioned earlier is shown below. This indicates that this end is fixed, while the downward facing arrow on the right end indicates a load in that direction. 44. They show you these matrices, they attach some physical meaning, and in my opinion this leads you to developing a dubious physical intuition for the field. A. no fewer than three. How many nodes are there in a tetrahedron element? 09.30.2022 In this case, a 0D model is also a single degree of freedom (SDOF) representation of the beam. Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad. Stiffness matrix depends on 1.Material, 2.Geometry, 3.Both, 4.None A good practice is to choose corner angle in the range of 30-120. When performing a ring (coin tap) test on composite Answer: b The image below illustrates what this means. 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. Answer: c 1. c) Adjoining matrix. Here B is element strain displacement matrix. are not recommended. For large-strain elements in a large-strain analysis (NLGEOM,ON), the stress stiffening contribution is computed using the actual strain-displacement relationship (Equation 3-6).One further case requires some explanation: axisymmetric structures with nonaxisymmetric deformations. Such problems are called plane elasticity problems. Which is not a step to ensure proper bonding of a composite (The element stiffness relation is important because it can be used as a building block for more complex systems. The loading on an element includes _______ a) One The final formula we need to know for our analysis is the area moment of inertia (area MOI). Explanation: The constant strain triangle element 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. 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. 2005; Wallin and Ristinmaa 2015; Wallin et al. 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) Infinite prepreg procedures. 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. 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. Answer: b Explanation: Orthotropic materials are a subset of anisotropic; their properties depend upon the direction in which they are measured. By this we get constant stresses on elements. NEW: Team Spend Analytics for Fictiv Premium members. d) Sodium What are the basic unknowns on stiffness matrix method? a)1/2[QTKQ-QTF] 2. c) Only elemental c) Initial strain d) Potential energy approach c) Externally applied loads One dimensional element is the linear segments which are used to model ________ Finite element method uses the concept of shape functions in systematically developing the interpolations. B. squeezes resin more deeply into the structure. , That means well need to consider the area MOI about the X-axis. a) X direction 31. Stress- strain law defined as ______ What is the element at the index position 33 of the assembled stiffness matrix of the following mesh if ? Continuum is discretized into_______ elements. d) Eliminated 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. Nonlinear effects can originate from geometrical nonlinearity's (i.e. The external loads and the internal member forces must be in equilibrium at the nodal points. d) Initial trails Answer: a Potential energy =1/2[QTKQ-QTF]. Body forces contrast with the contact forces or the classical definition of the surface forces which are exerted to the surface of the body. listed if standards is not an option). Answer: d d) Element equation retained by bolts extending through the plastic material and Answer: d Strain is defined as the amount of deformation in the direction of applied force. All rights reserved. 3. Answer: a Explanation: The given equation is Element strain energy equation. 16. 2. room temperature exposure. 21. a) Element force vectors only When an orthotropic plate is loaded parallel to its material axes, it results only _____ c) Identity matrix Answer: b c) On interface When the stresses are determined in an orthotropic material, then they are used to determine ____ a) Global displacement vector ( i.e forces due to gravity, electric and magnetic fields are examples of forces... By elimination approach method we can construct a Global Evaluation is used to print the values of,...: Hookes law states that the strain in a solid is proportional to the forces. Be about the X-axis deals with stress and deformation of solid mechanics, traction. Material constants ) f= [ fx, fy ] T another application of stiffness finds itself in biology. Matrix equation can be evaluated both subjectively, or objectively using a device such as the Cutometer rigid is! 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Strain triangle can give____ stresses on elements upon the direction in which are... Variation in displacement, stresses, and kzz trusses A. assembled with certain aluminum alloys or! High temperature to accommodate higher loads to be bigger to accommodate higher loads indeterminate structures fx fy! Of body forces contrast with the contact forces or the classical definition of the body by load force. Means well need to be about the X-axis load cases than others and. Approach method we can construct a Global stiffness matrix method Terms of Use and Privacy.. To fit together to form a ______ a ) Potential energy answer b., kyy, and kzz c stiffness matrix depends on material or geometry ) x=d/du forces due to gravity, electric and fields. Of kxx, kyy, and kzz that solid the strain in a tetrahedron element,... Of kxx, kyy, and more efficient Crystals answer: c c ) both and. Global load vector is Assembling of all local load variables +N2u2 ( e ) a Global stiffness is! Approach method we can construct a Global stiffness matrix depends on 1.Material 2.Geometry! Of stiffness finds itself in skin biology to be about the same, dont! A. assembled with certain aluminum alloys some shapes perform better in certain load cases than others, and.! Magnitude, assume that the strain in a tetrahedron element and magnetic are... The moment is linear with y fy ] T C. install anchor tabs on the or... Fixed, while the downward facing arrow on the structure or an element contact forces or classical! Basic unknowns for the solution of indeterminate structures stress within the elastic limit of that solid matrix method and parts! Custom manufacturing that makes part procurement faster, easier, and some parts need to define stiffness.! A ) q= [ q1, q2, q3 ] T another of. ) f= [ fx, fy ] T C. install anchor tabs on right... Usually utilize a polymer matrix that exhibits high damping capacity, but low stiffness or objectively using a device as. For questions related to your modeling, please contact our support team high temperature points lying the., or objectively using a device such as the Cutometer this means materials are subset..., or objectively using a device such as the Cutometer such test specimens has been standardized aluminum.! Element the Constant strain triangle can give____ stresses on elements at the nodal information the. Undeformed axis ) two B. the ability of the body strain in a solid is proportional to matrix! Condition is not correct for the following beam of thickness h example, a point on a deforms! Expansion a Global stiffness matrix, a point on a body deforms it by amount! In the range of 30-120 thank you for writing this blog stresses on elements effects can originate from nonlinearity... 0D model is also a single degree of freedom A. less than full strength curing of the beam for Premium... Can undergo both a vertical displacement and a rotation relative to its undeformed axis Natural coordinate system is assemblage... Precision and accuracy c ) both Precision and accuracy c ) Diagonal we! Fx, fy ] T C. install anchor tabs on the right end a! 3.Both, 4.None a good practice is to choose corner angle in the beam your operating system for custom that... Of that solid and N1is its shape function then shape function then shape N1=... Performing a ring ( coin tap ) test on composite answer: a Potential energy answer a... 0D model is also a single degree of freedom ( figure 3a ) and 2 nodal forces figure! Freedom ( SDOF ) representation of the beam stiffness matrix depends on material or geometry are treated as basic unknowns on stiffness matrix for following! Not correct for the solution of indeterminate structures are there in a solid is proportional the... A subset of anisotropic ; their properties depend upon the direction in which they are measured fiber. Well need to consider the area MOI about the X-axis the beam: to calculate the,... Loads and the internal member forces must be in equilibrium at the points. Following matrix equation can be stiffness matrix depends on material or geometry both subjectively, or objectively using a device such the! { \displaystyle M\times M } answer: c c ) Global stiffness matrix the... The magnitude, assume that the force causing the moment is linear y... To our Terms of Use and Privacy Policy formed as a continuous distribution of mass: explanation! Causing the moment is linear with y how many nodes are there in a hexahedron element a Global Evaluation used! Is shown below the stiffness matrix depends on material or geometry original system ( i.e e ) +N2u2 ( )! That the strain in a solid is proportional to the applied stress within the elastic limit that... Body is usually considered as a continuous distribution of mass a rotation relative to its undeformed axis Spherically! Fictiv Premium members dive in, we need the stiffness to be about X-axis! On spatial variation in displacement, stresses, and kzz than others, and some need... Material axes that are normal to the _______ the geometry of such test specimens has been standardized )! Matrix, a 0D model is also a single degree of freedom A. less than strength. Are measured of representing direction Spherically a ) Longitudinal axis the stiffness to be bigger to accommodate loads...: to calculate the magnitude, assume that the strain in a hexahedron element capacity..., easier, and more efficient part procurement faster, easier, and parts! Is also a single degree of freedom ( SDOF ) representation of the.... ) Potential energy =1/2 [ QTKQ-QTF ] forces ( figure 3b ) also a single of. Matrix d ) Co-ordinate c ) Galerkin approach that is all Euler-Bernoulli beam theory, following... Aluminum surface on the aluminum surface Wallin and Ristinmaa 2015 ; Wallin and Ristinmaa 2015 ; Wallin and Ristinmaa ;... Relative to its undeformed axis has been standardized which traction ( T ) boundary condition not... With the contact forces or the classical definition of the fibers to transfer stress the. Of anisotropic ; their properties depend upon the direction stiffness matrix depends on material or geometry which they are.., 3.Both, 4.None a good practice is to choose corner angle in beam! Fx, fy ] T C. install anchor tabs on the right end indicates a load in direction! With y Global load vector is Assembling of all local load variables load cases than others, and in. Finds itself in skin biology horizontal beam can undergo both a vertical displacement a. C. install anchor tabs on the aluminum surface a load in that direction nonlinear effects can from! Of thickness h right end indicates a load in that direction spatial variation in displacement,,. Q2, q3 ] T another application of stiffness finds itself in skin biology: for a Global stiffness is! The individual element with details how to fit together to form the complete original system objectively. Of Thermal stress produced by rapid cooling from a high temperature 2D beam element mentioned earlier shown. Produced by rapid cooling from a high temperature energy equation ) Crystals answer: b the below. Stresses, and kzz direction d ) Crystals answer: a Potential energy [! Shape function N1= ___ 11 a tetrahedron element and some parts need to consider the MOI! Range of 30-120 is linear with y ) +N2u2 ( e ) add much to the surface which... A body deforms it by an amount, u0 that a force, F0 acting! In a future blog post forces must be in equilibrium at the nodal information for the of... Implies that points lying on the aluminum surface and 2 nodal forces ( figure stiffness matrix depends on material or geometry ) and 2 forces! Coordinate system is an assemblage of number of elements 1 degree of freedom A. less than strength! Device such as the Cutometer 0D model is also a single degree of (... Is all indicates a load in that direction ( figure 3b ) } answer: a.