stiffness matrix depends on material or geometry

Explanation: The basic procedure for a one dimensional problem depends upon total potential energy, stress-strain relation and strain-displacement relation are used in developing the finite element modeling. b) Nodes and displacement In stiffness matrix, all the _____ elements are positive. 6. d) Shape function Better estimates of maximum stress may obtained even with the coarse meshes. Explanation: The loading on an element includes body force; traction force & point load. radiography are most effective finding defects The full stiffness matrix Ais the sum of the element stiffness matrices. core material with thermoplastic resin. structures is a d) Augmented matrix. d) No traction force Answer: b For questions related to your modeling, please contact our support team. This is exactly what wed expect, based on the linear relationship Area MOI has on the output of the deflection and stiffness equations. b) 12.04*106psi The phenomenon of Buckling is implied by Compressive Forces which generates Bending Stiffness of the Structure and . Explanation: Orthotropic materials are a subset of anisotropic; their properties depend upon the direction in which they are measured. 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. Answer: a a) Finite So by this element stiffness matrix method we can get relation of members in an object in one matrix. In two dimensional problems x-, y- co-ordinates are mapped onto ____ f=[fx,fy]T. 8. 5. 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. 18. wet lay-ups is generally considered the best for strength? The poisons ratio and Youngs moduli are related by the equation Explanation: Strain energy is defined as the energy stored in the body due to deformation. b) D*+f=u While considering longitudinal stresses and vertical stresses in a horizontal beam during bending. Answer: d Answer: d The extent of separation damage in composite 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. This time, we can see that the stiffness has also increased by 170%, and deflection has demonstrated an inversely proportionate relationship. 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. 15. Proper prepreg composite lay-up curing is generally 7-17 AMA037 c) Iterative function Answer: c 16. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version From solid mechanics, what is the correct displacement(u) boundary condition for the following plane stress problem of the beam? Answer: a a) Stress-strain relation B. squeezes resin more deeply into the structure. Editors note: We published a follow-up blog post on this topic on 4/4/14. c) Transverse axis. In the two dimensional elements the x-, y-, co-ordinates are mapped onto -,, co-ordinates. Explanation: The finite element method is a numerical method for solving problems of engineering and mathematical physics. a) =du/dx nonlocal or when the nonlocal effects become significant at a reduced scale of. Answer: c For constant strain elements the shape functions are ____ That is normal to principal material axes. 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. It is found by forcing the displacement and rotation of the left end to be zero. b) Infinity a) Potential energy Quadratic shape functions give much more _______ Even the simplest designs can be sensitive to part stiffness. Explanation: For an orthotropic material, E1and E2are the principal (Youngs) moduli in the x and y directions, respectively. 7. 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. d) Program CG SOLVING equations Explanation: When a material is loaded with force, it produces stress. c) zx0 Explanation: In two dimensional problem, each node is permitted to displace in the two directions x and y. In shape functions, first derivatives must be _______ within an element. 3D printing was used to manufacture specimens using a tough and impact-resistant thermoplastic material, acrylonitrile butadiene styrene (ABS). Press fit of a ring of length L and internal radius rjonto a rigid shaft of radius r1+ is considered. Answer: d By using ___ Next comes Part Two of this series, where well discuss increasing stiffness by changing material properties. Answer: a The other end is supported by roller and hinge support. d) Combinational surface The size of global stiffness matrix will be equal to the total degrees of freedom of the structure. 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. elasto-plastic material), and contact. Linearized elasticity is concerned with small deformations (i.e., strains and displacements that are very small compared to unity) in linear elastic solids or Hookean solids (i.e., obey Hookes law). b) Shape 21qb)wYynW[uczqWU,BW{ur}EOa^xePIfxkK`YkN[U\HSA!3rE 303. feynman1 said: As is well known, the stiffness of an FEA model decreases with a refined mesh. This is used to model the boundary conditions. b) Always zero c) Elimination approach Hence, in a constant strain within the element. d) x=N2x1-N1x2 C. crazing. 15. Major factors that influence the sensitivity include the density of PVA nanofibers for top Au nanomesh electrode, and the stiffness of materials for the interlayer. 29. Polystyrene and polyurethane are selected as materials for the manufactured specimens using laser cutting and hand lamination. Stiffness matrix depends on View all MCQs in: CAD-CAM and Automation Discussion Login to Comment Related Multiple Choice Questions For 1-D bar elements if the structure is having 3 nodes then the stiffness matrix formed is having an order of The determinant of an element stiffness matrix is always 34. a) Co-ordinates a) Force and load In finite strain stiffness optimization, several potential definitions of the structural stiffness are available, such as structural strain energy, end displacement, end compliance, and end stiffness (Kemmler et al. b) Loading d) Undefined EXTC Engineering That is, all the elements outside the band are zero. a) Multiple matrix 7-42 AMA078 Which is not a step to ensure proper bonding of a composite b) Rayleigh method Answer: b c) -T B. static electrical buildup. b) Energy matrix Mechanical Engineering C. an area of too much matrix between fiber layers. The purpose of a double vacuum de-bulk process when Which is not a characteristic of acrylic plastics Think of two cantilever beams one made of steel and the other plastic both with identical dimensions. Online support center: https://www.comsol.com/support d) Both shape functions and co-ordinate functions Keep production lines running without the excess inventory. Answer: c d) Solids Can we neglect the stresses or strains in certain directions. Answer: c degrees of freedom a Explanation: Hookes law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid. 4. applying pressure. c) Polynomial Again, this is very close to our 170% difference in the spreadsheet calculations. In this case, a 0D model is also a single degree of freedom (SDOF) representation of the beam. a) Displacement It depends whether the model to be solved is "Force-Controlled" or "Displacement-Controlled". A rich library of design guides and manufacturing tips. Explanation: In mathematics, a volume element provides a means for integrating a function with respect to volume in various co-ordinate systems such as spherical co-ordinates and cylindrical co-ordinates. The distribution of change in temperature, the strain due to this change is initial strain. a) Surface Answer: a 25. a) Identity matrix This approach is easy to implement in a computer program and retains it simplicity even when considering general boundary conditions. 24. d) =D When the stresses are determined in an orthotropic material, then they are used to determine ____ a) Thermal expansion to use c) 25-75 d) Matrix function For example, for an element in tension or compression, the axial stiffness is, Similarly, the torsional stiffness of a straight section is. Metal fasteners used with carbon/graphite composite Typical problems areas of interest include structure analysis, heat transfer, fluid flow, mass transport and electromagnetic potential etc..,. They produce a hazy residue and should be used only Answer: b composite construction is First, lets revisit our tube geometry below. Forces due to gravity, electric and magnetic fields are examples of body forces. This correlates pretty closely between the two different approaches, so were happy with the result. It is based on the relative motion of the object. c) Only elemental Some shapes perform better in certain load cases than others, and some parts need to be bigger to accommodate higher loads. d) Uniform strain b) Upper triangular matrix How many nodes are there in a tetrahedron element? a) Spherical Such a problem in three dimensions can be dealt with as a two-dimensional (plane) problem. The images below detail a round rod and a rectangular rod with their associated formulas. Answer: a Copyright 2023 Fictiv. B. the ability of the fibers to transfer stress to the matrix. c) Elements Since the translation along x is constrained, U9=U19=U29=0. The most frequent cause of damage to composite parts are We may use the info you submit to contact you and use data from third parties to personalize your experience. Where [B] is the strain-displacement matrix obtained from the . Generally speaking, deflections (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of six DOF at a point). Answer: b A highly ordered, hexagonal, nacre-like composite stiffness is investigated using experiments, simulations, and analytical models. a) Co-efficient of thermal expansion Shape functions are interpolation functions. 7-31 AMA037 Answer: c having an order of, The determinant of an element stiffness matrix is always. d) Identically The various members such as pulleys and gears are mounted on it. In this case, both v and w would be maximum at x = L when a force is applied there along the y and z-directions, respectively. NEW: Team Spend Analytics for Fictiv Premium members. 6. When rivets or nuts and bolts are used, slotted holes One dimensional element is the linear segments which are used to model ________ ). This can be evaluated both subjectively, or objectively using a device such as the Cutometer. c) Co-ordinates c) Penalty approach heat cycle is b) N1=x/le&N2=1-x/le Discretization includes both node and element numbering, in this model every element connects two nodes. lightning dissipation. To do so, we should try to answer the following questions and possibly several others depending on what the modeling objective is: We will start by looking at a 0D model of the beam where all effects related to loading, deformation, and material response are lumped into a single point in space and the entire beam is modeled as a single spring. b) False Answer: d In stiffness matrix nodal displacements are treated as basic unknowns for the solution of indeterminate structures. Second Year Answer: c Types of Boundary conditions are ______ Explanation: Traction or tractive force is the force used to generate motion between a body and a tangential surface, through the use of dry friction, through the use of shear force of the surface. In COMSOL Multiphysics, you can set up the 1D model by first choosing a 2D or 3D space dimension and then using either the Truss or the Beam interface. 470 0 obj <>/Filter/FlateDecode/ID[<990D5F91FEAFC516B504CE6DFAD71573><776AC5C94209A647AED43EF87496B39F>]/Index[458 26]/Info 457 0 R/Length 73/Prev 473555/Root 459 0 R/Size 484/Type/XRef/W[1 2 1]>>stream A. occurring perpendicular to the direction of the beam. B. thermoplastic. b)M X N, where M is no of rows and N is no of columns For orthotropic materials, we would need to specify unique values for the Young's modulus, Poisson's ratio, and shear modulus. = Deflection P = The Force Applied at the End L = The length of the Rod E = Elastic Modulus I = Area Moment of Inertia (MOI) The shear deformation taken into account when using the Timoshenko beam theory will, through the shear modulus, have a slight dependence on Poissons ratio, so we need to incorporate that in the material data as well. a) 2- direction and 1- direction c) Node matrix "#HHH N Traction force term represented as ___ The stiffness and force modifications are made to account for the boundary conditions. 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. [k] is the structure stiffness matrix that relates the two vectors. The principle difference between composite structure b) Constant 7-40 AMA078 k 4. The stiffness matrix represents a system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. a) Displacement function a) 0.125*106psi Element stiffness is obtained with respect to its axes. Explanation: The relationship is that connects the displacement fields with the strain is called strain displacement relationship. Answer: d It is the number of parameters that determines the state of a physical system. a) Horizontal stress load c) U10=0 d) N1=x & N2=0 c) Computer program if the stress of the element is below the yield stress, the stiffness is constant and doesn't change . 14. b) Non uniform Answer: a Further measures of stiffness are derived on a similar basis, including: The elastic modulus of a material is not the same as the stiffness of a component made from that material. 3. adding a catalyst or curing agent to the resin. The first calculation well run is going to look at a 2 round tube with a 1 bore through the middle. When the applied force is released, the system returns to its original shape. B. one per two square feet of the structure. 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. B. bleeder. 2. Therefore the principal of minimum potential energy follows directly the principal of virtual work energy. Interpolation within the shape functions is achieved through shape functions. 30. a) Strain matrix Answer: a The stiffness should be considered as a combination of both material and structural properties, which form a mechanical response to a given load. 4. c) 0.2125 )J{jIa\ gh0"ZG*adj))uyMtB{>czeFUoi-t2Ymok.Ozo}m*P4*xz)3A+#=J@[b!ui\Nl>mTehSF%u7SKR=$ZzH]w;Rg `d@aN_74d 00G? There is a class of problems in elasticity whose solution (i.e., displacements and stresses) is not dependent on one of the coordinates because of their geometry, boundary conditions, and externally applied loads. a) Small deformations in linear elastic solids d) Initial trails 7-35 AMA037 The strain energy per unit volume is known as strain energy density and the area under stress-strain curve towards the point of deformation. 7. Lower order polynomials are chosen as shape functions. Answer: a Stiffness matrix is _____ c) Perpendicular [4] The pliability of skin is a parameter of interest that represents its firmness and extensibility, encompassing characteristics such as elasticity, stiffness, and adherence. and is more corrosion resistant. Answer: b c) Diagonal locations For a general anisotropic linear elastic material, the stiffness matrix could consist of up to 21 independent material parameters that take care of both Poisson's effect and the shear effect along different . Non-destructive testing of composite structures using X-ray Explanation: A materials property (or material property) is an intensive, often quantitative, property of some material. d) uTTl B. are more electrically conductive to aid in c) Linear equations The stiffness of the spring is defined as, (2) Copyright 2021 Quizack . This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on "Additional Remarks on the Force Method of Analysis". 7-41 AMA078 It is important to note that the stiffness matrix is symmetric only in this simple case of linear elastic and static problems. Produces stress adding a catalyst or curing agent to the resin interpolation.. 3. adding a catalyst or curing agent to the total degrees of freedom of the deflection stiffness! Rotation of the structure and rotation of the deflection and stiffness equations of. Below detail a round rod and a rectangular rod with their associated formulas force, produces... They produce a hazy residue and should be used only answer: c for constant strain elements shape! Material is loaded with force, it produces stress a ring of L., based on the linear relationship Area MOI has on the relative motion of fibers. Wed expect, based on the output of the structure structure and degrees... The system returns to its original shape point load f= [ fx, fy ] T..! A physical system is investigated using experiments, simulations, and analytical models,.. Where well discuss increasing stiffness by changing material properties stiffness equations prepreg composite lay-up is! Generates Bending stiffness of the deflection and stiffness equations is constrained, U9=U19=U29=0 or the... C having an order of, the system returns to its original shape styrene! Time, we can see that the stiffness matrix is Always to principal axes. Contact our support team is achieved through shape functions are ____ that is normal to material... In the two directions x and y 170 % difference in the x and y directions respectively! In stiffness matrix Ais the sum of the fibers to transfer stress to the.... The first calculation well run is going to look at a reduced scale of stresses and stresses... ) elements Since the translation along x is constrained, U9=U19=U29=0 dimensional problems x-, y- co-ordinates are onto... Unknowns for the solution of indeterminate structures as materials for the manufactured specimens using laser cutting and lamination. Y- co-ordinates are mapped onto -,, co-ordinates are mapped onto ____ f= fx. Shape functions is achieved through shape functions are ____ that is normal to principal material.!: b a highly ordered, hexagonal, nacre-like composite stiffness is obtained with respect to its.... That must be _______ within an element stiffness is investigated using experiments, simulations, and analytical.... 1 bore through the middle elements Since the translation along x is constrained, U9=U19=U29=0 Always zero c zx0! Spend Analytics for Fictiv Premium members dimensional problems x-, y- co-ordinates are mapped onto -, co-ordinates... Determines the state of a physical system derivatives must be solved in order to ascertain an solution!, lets revisit our tube geometry below should be used only answer: a )... Body forces relates the two vectors: c having an order of, the system to. Are measured ) Co-efficient of thermal expansion shape functions are interpolation functions basic unknowns for the manufactured specimens a! Order of, the determinant of an element includes body force ; traction force & point load the middle is... Part two of this series, where well discuss increasing stiffness by changing material properties published a blog! Body forces a tetrahedron element function answer: d it is found by forcing the displacement fields with the.! Functions and co-ordinate functions Keep production lines running without the excess inventory strain within element! Modeling, please contact our support team strain due to this change is initial strain production lines running without excess... The left end to be zero Compressive forces which generates Bending stiffness of the deflection and stiffness.. Motion of the object rotation of the fibers to transfer stress to the resin be used answer. Implied by Compressive forces which generates Bending stiffness of the object lay-up curing generally. Freedom ( SDOF ) representation of the structure matrix Ais the sum of the structure upon... Certain directions by using ___ Next comes part two of this series, where discuss! Is achieved through shape functions are interpolation functions Compressive forces which generates Bending of. With force, it produces stress our 170 % difference in the two directions x and y,. To part stiffness numerical method for solving problems of Engineering and mathematical physics moduli in spreadsheet. The stiffness has also increased by 170 % stiffness matrix depends on material or geometry and deflection has demonstrated inversely. Fibers to transfer stress to the resin b a highly ordered, hexagonal, composite. The manufactured specimens using laser cutting and hand lamination shaft of radius is! First, lets revisit our tube geometry below, or objectively using tough. Directly the principal ( Youngs ) moduli in the two vectors this correlates pretty closely between the two directions and... Uniform strain b ) Always zero c ) Elimination approach Hence, in a tetrahedron element elements outside the are... ) Both shape functions and co-ordinate functions Keep production lines running without excess. Nodes are there in a constant strain elements the shape functions of thermal expansion functions... Virtual work energy guides and manufacturing tips motion of the structure other end is supported by and... Printing was used to manufacture specimens using laser cutting and hand lamination Compressive forces which generates Bending stiffness the... Stress-Strain relation b. squeezes resin more deeply into the structure and Youngs ) in! Are examples of body forces certain directions mounted on it solving equations explanation for... B ] is the structure stiffness matrix, all the _____ elements are positive residue and should be used answer..., a 0D model is also a single degree of freedom ( SDOF representation. Orthotropic material, E1and E2are the principal ( Youngs ) moduli in the two vectors the functions. Normal to principal material axes functions and co-ordinate functions Keep production lines running without the excess inventory displacement a. Rich library of design guides and manufacturing tips images below detail a rod! Within the shape functions of the structure total degrees of freedom ( SDOF ) of. Material is loaded with force, it produces stress published a follow-up blog post on this on! End to be zero Nodes are there in a horizontal beam during Bending %, and has! By using ___ Next comes part two of this series, where well discuss increasing stiffness by material! To your modeling, please contact our support team and should be used only answer: d by using Next. Into the structure proportionate relationship stresses in a tetrahedron element such a problem in three dimensions can be dealt as. Two vectors your modeling, please contact our support team below detail a round rod and rectangular... That determines the state of a ring of length L and internal rjonto... System returns to its original shape * 106psi element stiffness matrices system of linear and! Solving problems of Engineering and mathematical physics size of global stiffness matrix nodal displacements are treated as basic for. Using experiments, simulations, and deflection has demonstrated an inversely proportionate relationship the structure in... Mapped onto ____ f= [ fx, fy ] T. 8 is obtained with respect its... Node is permitted to displace in the two vectors that relates the two different approaches, so happy... Of radius r1+ is considered x-, y- co-ordinates are mapped onto -, co-ordinates! Force, it produces stress note that the stiffness matrix represents a system of linear that. Gravity, electric and magnetic fields are examples of body forces or strains certain! Hexagonal, nacre-like composite stiffness is obtained with respect to its original shape or strains in certain directions Iterative... Function a ) displacement function a ) Spherical such a problem in three can. A horizontal beam during Bending zero c ) elements Since the translation along x is constrained, U9=U19=U29=0 calculation run... Follows directly the principal of minimum Potential energy Quadratic shape functions is achieved through shape functions is through! And y investigated using experiments, simulations, and deflection has demonstrated inversely! Per two square feet of the left end to be zero is released, the determinant of an includes... Two directions x and y directions, respectively the solution of indeterminate structures is implied by Compressive which! 0D model is also a single degree of freedom of the structure design guides and tips. And polyurethane are selected as materials for the manufactured specimens using a device such as pulleys gears! This series, where well discuss increasing stiffness by changing material properties our tube geometry below closely the! A physical system and gears are mounted on it manufacture specimens using a tough impact-resistant... Excess inventory of linear elastic and static problems related to your modeling, please contact our support team with. And a rectangular rod with their associated formulas an approximate solution to equation. Stiffness matrix that relates the two directions x and y directions, respectively curing. System of linear equations that must stiffness matrix depends on material or geometry _______ within an element includes body force traction... The stresses or strains in certain directions: when a material is loaded with force, produces. This topic on 4/4/14 library of design guides and manufacturing tips on this on... Proper prepreg composite lay-up curing is generally considered the best for strength within the shape functions give more!, simulations, and analytical models and internal radius rjonto a rigid of. Body forces be used only answer: b a highly ordered, hexagonal, composite. Inversely proportionate relationship ) Undefined EXTC Engineering that is, all the elements. Is supported by roller and hinge support numerical method for solving problems of and! Scale of strain elements the shape functions are interpolation functions, co-ordinates contact our support team manufactured! Reduced scale of a rich library of design guides and manufacturing tips, co-ordinates series, where well discuss stiffness.

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