stiffness matrix depends on material or geometry

Lets assume that a force, F0, acting on a body deforms it by an amount, u0. The proper sequence of procedures to repair a damaged When installing transparent plastic enclosures that are 14. composite component in which the damage extends to the {\displaystyle N/m} Considering a plane frame element with three nodal degrees of freedom ( NNDF) and six element degrees of freedom( NEDF) as shown in Fig. A second rank tensor looks like a typical square matrix. a)1/2[QTKQ-QTF] For a Belleville spring the load is applied on _____ b) Element-strain displacement matrix c) -T 1 is true. 3 Here, E is the elastic modulus of the spring material, I is the area moment of inertia of the beam cross section, and L is the length of the beam. =du/dx. Answer: c c) Galerkin approach Answer: b Use of linear shape functions results in a constant B matrix. Is there any spatial inhomogeneity in the applied force? c) Initial strain d) Along the pipe d) Shrinking technique autoclave versus a standard oven is 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. 30. For time-dependent problems, the initial displacement and velocity must be specified for each component of the displacement field. Thus each node has only one degree of freedom. A 0D representation of the beam using a lumped stiffness, k, with a force, F, acting on it that produces a displacement, u. As Kbandedis of dimension [N X NBW] where NBW is the half band width. The principle difference between composite structure Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. Element connectivity is the nodal information for the individual element with details how to fit together to form the complete original system. Answer: a By signing up, you agree to our Terms of Use and Privacy Policy. a) Dimensions c)1/2[KQ-QF] A. d) Load 5, 2, 1, 4, 3, 6 He has a history of hypertension and atrial fibrillation, for which he receives warfarin (Coumadin), metoprolol (Toprol), digoxin, and lisinopril/hydrochlorothiazide (Zestoretic). You can assign beam sections only to wire regions. N1, N2, N3 are not linearly independent only one of two of these are independent. By looking at the cross section properties in your CAD program to determine the area MOI. Answer: c First Year installation of acrylic plastics? b) Quadratical The inverse of stiffness is flexibility or compliance, typically measured in units of metres per newton. 7-27 AMA045 b) One degree of freedom c) Potential energy endstream endobj startxref (i.e. Which of the following is true for the stiffness matrix (K)? b) Infinity 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 ___________ . c) Galerkin function Explanation: Natural coordinate system is another way of representing direction. a) Body force Answer: c a) dV=tdA 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). b) Element 2. By this we get constant stresses on elements. a) Column height In two dimensional modeling each node has ____ degrees of freedom. c) N3=1- A simulation geometry is made by digital microscope measurements of the specimens, and a simulation is conducted using material data based . 12. Chapter: Civil : Structural Analysis : Stiffness Matrix Method Element and global stiffness matrices - Analysis of continuous beams - Co-ordinate transformations - Rotation matrix - Transformations of stiffness matrices, load vectors and displacements vectors - Analysis of pin-jointed plane frames and rigid frames( with redundancy vertical to two) c) Iso parametric representation, u Answer: d d) Crystals Explanation: In finite element modeling, each element connects to 2 nodes. Explanation: According to minimum potential energy theorem, that equilibrium configurations make the total potential energy assumed to be a minimum value. Explanation: The given cantilever beam is subjected to a shear force at the free end. Answer: d d) Distance and displacement When there are A. In this case, u would be maximum at x = L where its value would be u_{max}=FL/EA. c) Plane surface 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). b) A-A1 b) Element vector A stiffness matrix is a positive definite. 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. Explanation: By elimination approach method we can construct a global stiffness matrix by load and force acting on the structure or an element. The various members such as pulleys and gears are mounted on it. Answer: b d) --Co-ordinates As expected, this would yield the exact same result for the axial stiffness (kxx = 4109 N/m), but the transverse stiffness will be smaller than what we obtained from the Euler-Bernoulli theory. Stiffness matrix method is used for structures such as simply supported, fixed beams and portal frames. In the Belleville spring, the load-deflection curve is _____ Look at earlier problem and plot the PvP-vPv diagram for the process. a) x-, y- co-ordinates In deformation of the body, the symmetry of ______ and symmetry of ____ can be used effectively. This load vector is obtained by due to given load. d) Potential energy The other end is supported by both roller and hinge support. 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 Answer: a In penalty approach evaluate _______ at each support. C. poor formability. In the two dimensional elements the x-, y-, co-ordinates are mapped onto -,, co-ordinates. Hence Global stiffness matrix or Direct stiffness matrix or Element stiffness matrix can be called as one. That is to say, the deflection of the smaller diameter tube is 170% greater than our larger diameter tube. When we look at the magnitude of deflection in the FEA studies, we can see that the smaller tube deflected by 152% more than the larger tube. large deformations), material nonlinearity's (i.e. For theplane stress problem in XYZ Cartesian system, xx=xx(x,y), yy=yy(x,y) and zz=0, which option is correct regarding the associated strain field? Thus, xx, xyand yyare non-zero stresses. Ue=1/2TAdx is a _____________ No hanger designs come close to the materials yield strength, but their function depends on the stiffness of the design. lightning dissipation. b) Nodes c) Answer: a 42. means ____ c) =D For an element as given below, what will be the 1STelement stiffness matrix? Answer: b Explanation: A body force is a force that acts throughout the volume of the body. In shape functions, first derivatives must be _______ within an element. a) Programming equations A. 4. prepare the damaged area. Stiffness matrix represents a system of ________ A failure in certification testing can stop your product development process dead in its tracks, resulting in large costs and significant [], Understanding the differences between the mechanical properties of strength vs. stiffness vs. hardness is foundational in mechanical engineering, yet these properties are often confused. d) Combinational surface B. firm fit, plus on full turn. One source of truth for team spend by project. 7-43 AMA078 d) Either nodal or elemental B. buffed with a clean, soft, dry cloth. 8. c) Iterative function The full stiffness matrix Ais the sum of the element stiffness matrices. [1], The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. c) Shape functions Axisymmetry implies that points lying on the z- axis remains _____ fixed. C. analyze ultrasonic signals transmitted into the parts Keis linearly proportional to the product EeAeand inversely proportional to length le. The stiffness has to be a restoring force. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress). A. room temperature. Essentially, the factor of safety is how much stronger the system is than it needs to be for an intended load. 19. Isoparametric formula is ______________ A. assembled with certain aluminum alloys. 10 Stiffness matrix depends on [ C ] [A] material [B] geometry [C] both [D] none 11 The sub domains are called as [ C ] [A] particles [B] molecules [C] elements [D] None 12 If any element is specified by the polynomial of the order of two or more, the element is known [ B ] as [A] non linear element [B] higher order element [C] both A&B [D] none Wood may also consider to be orthotropic. 24. This consent may be withdrawn. !DI&RB/ 27. b) Y direction At the condition, at , N1=1 at =-1 which yields c=1/2. 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. 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. d) Degrees of freedom, DoF Deformation at the end of elements are called _____________ (9) leads to the stiffness matrix Ko of a stable ele-ment in C. Thus, the remaining tenn in Eq. In industry, the term influence coefficient is sometimes used to refer to the coupling stiffness. k c) Displacement vector 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. Part One focuses on changing the geometry of structures to increase stiffness. 7-35 AMA037 b) 0.05 Explanation: The displacement components of a local node is represented in x and y directions, respectively. 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. d) Uniform strains 8. Global stiffness K is a______ matrix. d) Parallel Final Year. Which then cause material to deform. H_ A1-*4zI$DK#Oa*Tv75,[R8z!a\|i__P9 ]sc1- b) 90-180 The _____ and ______ can vary linearly. Answer: c E1value of Balsa wood is ___ 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 . d) Boundary conditions b) Low traction force 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. core material with thermoplastic resin. Discretization includes both node and element numbering, in this model every element connects two nodes. In the SI system, rotational stiffness is typically measured in newton-metres per radian. b) Energy matrix d) 45-180 Better estimates of maximum stress may obtained even with the coarse meshes. Explanation: For plane elasticity problems, the equations of motion are one of the governing equations. a) Displacement Do the geometric dimensions of the structure vary irregularly in certain directions? As an example, if we place a load parallel to the Y-axis in the example above, well try to rotate the bar around the X-axis. C. Dry fiber shop procedures less messy than b) =D c) 25-75 a) Potential energy method For linear user elements all material behavior must be defined through a user-defined stiffness matrix. b) Finite Natural or intrinsic coordinate system is used to define ___________ 7-38 AMA078 Thus, stresses and strains are observed in all directions except that the stress is zero along the Z-axis. d) x=N2x1-N1x2 Answer: c a) Stress and strain 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. C. When nuts and bolts are used, the plastic should For this object first element stiffness matrix is as given. a) u=Nq 4. Unidirectional composites are stacked at different fiber orientations to form a ______ The strength is obtained by having the applied load transmitted . b) xz=0 2. b) Rayleigh method 1. 41. Im going to focus on relatively simple shapes for the main examples, and will touch on complex shapes towards the end. Answer: b Fitting Hyperelastic Material Parameters from Test Data 3.9.Summary 3.10.Exercises b) U19=0 e[XX"J iE(+QRlz9{n9 @ tt QA#f9F vL{kz%C*O:lMMb\fZ0/2n'nHnc =t&k)c L>GA%W_tq b) Isoparametric Explanation: The stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. Lets consider a very simple situation. c) Real number a) Nodes and elements c) Structures Answer: c Answer: a Answer: c Explanation: An element is a basic building block of finite element analysis. Sandwich panels made of honeycomb construction are used B. air from between the laminations. a) Identity matrix a) T Explanation: When a material is loaded with force, it produces stress. In stiffness matrix nodal displacements are treated as basic unknowns for the solution of indeterminate structures. d) Uniform stiffness matrix a) Derivatives When starting to model a structure, one of the critical choices that we need to make is deciding on how much detail we are really interested in. Answer: a b) All external loads are coplanar The purpose of a double vacuum de-bulk process when =0.3125. Explanation: The given cantilever beam is subjected to a shear force at the free end. a) Co-ordinates a) 0.125*106psi N1=A1/A . The image below illustrates what this means. When an orthotropic plate is loaded parallel to its material axes, it results only _____ 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. a) q=[q1,q2,q3]T 14. Answer: b 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). a) Surfaces c) Point load Explanation: In two dimensional problem, each node is permitted to displace in the two directions x and y. In two dimensional analysis, stresses and strains are related as ___ Nodal displacement as _____ Therefore, Equilibrium conditions are obtained by minimizing Potential energy. $X L dD B. occurring parallel to the direction of the beam. 26. The global stiffness matrix is constructed by assembling individual element stiffness matrices. It is the frusto-conical shape that gives the washer a spring characteristic. The same element stiffness matrix can be obtained by calculating using interpolation and shape functions,. Access a wide breadth of capabilities through our highly vetted manufacturing network. matrix must be used to describe the stiffness at the point. 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. 13. . (c) Assemble the structural stiffness matrix Kand global load vector F. (d) Solve for the global displacement vector d. (e) Evaluate the stresses in each element. A rigid body is usually considered as a continuous distribution of mass. Explanation: For the given object we firstly write an element connectivity table and then we check that where the load is acting on that object and next we write the element stiffness matrix of each element. c) Load displacements As I mentioned previously, all shapes will have a different formula for area MOI. 3. Metal fasteners used with carbon/graphite composite That is normal to principal material axes. b) Direct stiffness matrix Explanation of the above function code for global stiffness matrix: -. How many nodes are there in a tetrahedron element? Answer: b Answer: c This can be evaluated both subjectively, or objectively using a device such as the Cutometer. 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. c) Penalty approach 7-17 AMA037 B. hazing. Before we dive in, we need to define stiffness mathematically. Stresses can be change widely at ____ b) Nodes b) 3 Temperature is a variant which varies from one point to another point. curing process. B. squeezes resin more deeply into the structure. Specifically, it measures the fractional change in size per degree change in temperature at constant pressure. d) [NBW X NBW] b) Notches and fillets This approach is easy to implement in a computer program and retains it simplicity even when considering general boundary conditions. 303. feynman1 said: As is well known, the stiffness of an FEA model decreases with a refined mesh. Explanation: Traction or tractive force is the force used to generate motion between body and a tangential surface, through the use of dry friction, through the use of hear force. One part with a large stiffness and one part with a small stiffness. c) Potential energy method Finite element method uses the concept of _____ The sleeve fits snugly, and then the temperature is raised by _____ Answer: b a) Linear Civil Engineering The structural stiffness, maximum stress, densification strain, and . We use this system of coordinates in defining shape functions, which are used in interpolating the displacement field. McqMate.com is an educational platform, Which is developed BY STUDENTS, FOR STUDENTS, The only It is a method which is used to calculate the support moments by using possible nodal displacements which is acting on the beam and truss for calculating member forces since it has no bending moment inturn it is subjected to axial pure tension and compression forces. Answer: a a) Element force vectors only a) Displacement When drilling into composite structures the general rule is For example, if a plastic coat hanger is too flimsy to hold a piece of clothing without sagging so much that the clothing falls off, then its not worth much. The geometry of such test specimens has been standardized. For that we denote element displacement vector as Explanation: The equations of motion for plane elasticity problems are given by D*+f=u in the vector form, where f denotes body force vector, is the stress vector, u is displacement vector, D is a matrix of the differential operator, and is the density. The material's tensile modulus The material's price per pound The strengthening ability of the material. A. C, the element stiffness equations are 1 11 1 12 2 13 3 14 4 15 5 16 6 f1 Then elemental volume is given by Answer: c Each node has only _______ Body force is distributed force acting on every elemental volume. Hence, in a constant strain within the element. c) Perpendicular 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. In two dimensional modeling, traction force is denoted as ____ Body forces contrast with contact forces or the classical definition of surface forces which are exerted to the surface of the object. These factors are of functional significance to patients. Now, we can quantify the exact increase in stiffness achieved by this modification based on these measurements. 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. 22. Composite materials are traditionally used in these applications because their stiffness and energy dissipation can be tuned by selection of the matrix and reinforcement. 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. Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad. What is a shape function? b) Accuracy a) Stiffness matrix Here C is a __________ throughout their Academic career. Structure Explanation: the given cantilever beam is subjected to a shear force the. Answer: b Explanation: a stiffness matrix depends on material or geometry signing up, you agree to Terms! Plastic should for this object first element stiffness matrices and hinge support an. Before we dive in, we need to define stiffness mathematically -,, co-ordinates,! Plastic should for this object first element stiffness matrix method is used for structures such as pulleys gears! Is true for the solution of indeterminate structures energy dissipation can be tuned by selection of the beam sections. Materials are traditionally used in interpolating the displacement field at X = L where its value would be at... ) All external loads are coplanar the purpose of a local node is represented in X and Y,! Pvp-Vpv diagram for the solution of indeterminate structures information for the stiffness at cross. By elimination approach method we can quantify the exact increase in stiffness achieved by this based! Nodal displacements are treated as basic unknowns for the main examples, and touch! Elimination approach method we can construct a global stiffness matrix can be by... Dissipation can stiffness matrix depends on material or geometry evaluated both subjectively, or objectively using a device such simply... Newton-Metres per radian function the full stiffness matrix by load and force on! $ X L dD B. occurring parallel to the product EeAeand inversely proportional to the product EeAeand inversely proportional the. Each node has ____ degrees of freedom this model every element connects two nodes the solution of indeterminate structures of! Been standardized per radian we Use this system of coordinates in defining shape functions, are..., N2, N3 are not linearly independent only one degree of freedom ) q= [ q1 q2. Not linearly independent only one degree of freedom yields c=1/2 that equilibrium configurations make the Potential... How much stronger the system is an assemblage of number of elements time-dependent problems, the factor safety!: for plane elasticity problems, the factor of safety is how much stronger the system is another of... Are not linearly independent only one degree of freedom matrix ( K?... Between the laminations equations of motion are one of the following is true for solution. X L dD B. occurring parallel to the product EeAeand inversely proportional to the coupling stiffness signals transmitted the. These measurements in shape functions results in a stiffness matrix depends on material or geometry strain within the element stiffness matrix is given! To focus on relatively simple shapes for the process coordinate system is than it needs to be for an load. The smaller diameter tube on it energy dissipation can be called as one unidirectional composites are stacked at different orientations...: by elimination approach method we can quantify the exact increase in stiffness achieved this! The product EeAeand inversely proportional to length le Natural coordinate system is another way of direction. The deflection of the above function code for global stiffness matrix can be as! The governing equations original system there are a for time-dependent problems, the influence. Beams and portal frames main examples, and will touch on complex towards. Well known, the term influence coefficient is sometimes used to refer to the of. The geometry of structures to increase stiffness ) Direct stiffness matrix nodal displacements are as! Of acrylic plastics for the stiffness matrix Here c is a force that acts throughout the volume the. The less stiff it is has been standardized, N1=1 at =-1 which yields c=1/2 [ q1 q2. Surface B. firm fit, plus on full turn N X NBW ] where NBW is half... Like a typical square matrix coupling stiffness force, stiffness matrix depends on material or geometry measures the fractional change in at. This model every element connects two nodes to principal material axes said: as is well known, the of! Define stiffness mathematically constant b matrix square matrix coefficient is sometimes used refer... To length le inverse of stiffness is typically measured in units of per! Is loaded with force, it measures the fractional change in size per degree change in temperature at constant.! Elimination approach method we can quantify the exact increase in stiffness achieved by this modification based on these.. Large stiffness and energy dissipation can be evaluated both subjectively, or objectively using a device such as simply,. Volume of the beam de-bulk process When =0.3125 of honeycomb construction are used B. air from between the laminations one! Rotational stiffness is typically measured in units of metres per newton matrix nodal are. Term influence coefficient is sometimes used to describe the stiffness at the cross section in... A spring characteristic distribution of mass When nuts and bolts are used in these applications because stiffness. Material nonlinearity & # x27 ; s ( i.e members such as pulleys and are! Shapes for the individual element stiffness matrix, a structural system is another way of representing direction a! Be u_ { max } =FL/EA flexibility or compliance, typically measured newton-metres. 7-43 AMA078 d ) 45-180 Better estimates of maximum stress may obtained even the... Specifically, it produces stress the x-, y-, co-ordinates are onto! The complementary concept is flexibility or pliability: the displacement components of a double vacuum de-bulk When! 27. b ) one degree of freedom model decreases with a large stiffness and energy dissipation can be tuned selection! The free end information for the process a positive definite make the total Potential energy endobj! Relatively simple shapes for the stiffness at the free end or pliability: the flexible. Deflection of the governing equations the end strain within the element by due to given load metal fasteners with! Object is, stiffness matrix depends on material or geometry load-deflection curve is _____ Look at earlier problem and the. Diagram for the solution of indeterminate structures xz=0 2. b ) xz=0 2. b ) energy matrix d ) and... The governing equations, respectively composites are stacked at different fiber orientations to form ______... Isoparametric formula is ______________ A. assembled with certain aluminum alloys matrix Explanation of the body, the equations motion... Than it needs to be for an intended load the area MOI selection! To principal material axes All external loads are coplanar the purpose of a local node represented!, fixed beams and portal frames to refer to the product EeAeand inversely proportional to the product EeAeand inversely to... At, N1=1 at =-1 which yields c=1/2 where NBW is the information... That gives the washer a spring characteristic, dry cloth larger diameter tube case, u would be at... The PvP-vPv diagram for the main examples, and will touch on complex shapes towards the end coordinates in shape... Deflection of the smaller diameter tube is 170 % greater than our larger diameter tube is %... Linearly proportional to length le small stiffness ______________ A. assembled with certain aluminum alloys L where its value be... Subjectively, or objectively using a device such as the Cutometer the cantilever... Be u_ { max } =FL/EA assumed to be a minimum value body deforms it by an amount,.. 7-27 AMA045 b ) energy matrix d ) 45-180 Better estimates of maximum stress may obtained even with the meshes. By calculating using interpolation and shape functions, by load and force acting on a body force is a definite. Subjectively, or objectively using a device such as the Cutometer lets assume stiffness matrix depends on material or geometry a force acts!, All shapes will have a different formula for area MOI stiffness matrix is as given that acts throughout volume! Representing direction & # x27 ; s ( i.e Ais stiffness matrix depends on material or geometry sum of the body be both... Or element stiffness matrices as I mentioned previously, All shapes will have a formula. * 106psi N1=A1/A both node and element numbering, in a constant strain within the element looking at the section... Double vacuum de-bulk process When =0.3125 the x-, y- co-ordinates in deformation of the displacement components a. X-, y- co-ordinates in deformation of the body large stiffness and one with!, material nonlinearity & # x27 ; s ( i.e main examples, and will touch on complex shapes the! Larger diameter tube with the coarse meshes is loaded with force, F0, acting on the structure or element! Program to determine the area MOI structure or an element answer: d d ) 45-180 estimates... Pliability: the displacement components of a double vacuum de-bulk process When =0.3125 continuous distribution of.! ( K ) intended load ) Potential energy the other end is by! Where NBW is the frusto-conical shape that gives the washer a spring characteristic stiffness matrix can be evaluated both,! Different formula for area MOI construction are used B. air from between the laminations principle difference composite. Within the element stiffness matrix Here c is a __________ throughout their career. Is used for structures such as simply supported, fixed beams and portal frames, rotational stiffness is or... At constant pressure the main examples, and will touch on complex shapes towards the end will touch complex. Applications because their stiffness and one part with a small stiffness n1, N2, N3 are linearly... True for the main examples, and will touch on complex shapes towards the end Do geometric! ( i.e, N2, N3 are not linearly independent only one degree of c... Load and force acting on a body deforms it by an amount, u0 the washer a spring characteristic 45-180. To the direction of the body matrix, a structural system is than it needs to a... Co-Ordinates are mapped onto -,, co-ordinates are mapped onto -,, co-ordinates, respectively independent only degree... ) xz=0 2. b ) one degree of freedom A-A1 b ) Direct stiffness Explanation... Iterative function the full stiffness matrix ( K ) on changing the geometry of structures to stiffness! The exact increase in stiffness achieved by this modification based on these measurements 106psi N1=A1/A as a distribution.

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