dimension of global stiffness matrix is

2 The spring constants for the elements are k1 ; k2 , and k3 ; P is an applied force at node 2. 0 x Then the stiffness matrix for this problem is. Once all of the global element stiffness matrices have been determined in MathCAD , it is time to assemble the global structure stiffness matrix (Step 5) . z z 45 26 0 0 Note that the stiffness matrix will be different depending on the computational grid used for the domain and what type of finite element is used. c) Matrix. Apply the boundary conditions and loads. 0 In particular, for basis functions that are only supported locally, the stiffness matrix is sparse. u_i\\ For the spring system shown in the accompanying figure, determine the displacement of each node. , Explanation of the above function code for global stiffness matrix: -. k k 0 1000 lb 60 2 1000 16 30 L This problem has been solved! After inserting the known value for each degree of freedom, the master stiffness equation is complete and ready to be evaluated. y 4. The size of global stiffness matrix will be equal to the total degrees of freedom of the structure. We return to this important feature later on. 2 s L u One then approximates. Since there are 5 degrees of freedom we know the matrix order is 55. 21 0 The unknowns (degrees of freedom) in the spring systems presented are the displacements uij. 11. This means that in two dimensions, each node has two degrees of freedom (DOF): horizontal and vertical displacement. 65 2 To subscribe to this RSS feed, copy and paste this URL into your RSS reader. [ ] ] It is . 2 Q c The element stiffness matrix can be calculated as follows, and the strain matrix is given by, (e13.30) And matrix is given (e13.31) Where, Or, Or And, (e13.32) Eq. 0 Q When the differential equation is more complicated, say by having an inhomogeneous diffusion coefficient, the integral defining the element stiffness matrix can be evaluated by Gaussian quadrature. c \end{Bmatrix} Learn more about Stack Overflow the company, and our products. See Answer piecewise linear basis functions on triangles, there are simple formulas for the element stiffness matrices. L It was through analysis of these methods that the direct stiffness method emerged as an efficient method ideally suited for computer implementation. (b) Using the direct stiffness method, formulate the same global stiffness matrix and equation as in part (a). 1 7) After the running was finished, go the command window and type: MA=mphmatrix (model,'sol1','out', {'K','D','E','L'}) and run it. Although it isnt apparent for the simple two-spring model above, generating the global stiffness matrix (directly) for a complex system of springs is impractical. The size of the matrix depends on the number of nodes. 0 (M-members) and expressed as (1)[K]* = i=1M[K]1 where [K]i, is the stiffness matrix of a typical truss element, i, in terms of global axes. 2 The global stiffness relation is written in Eqn.16, which we distinguish from the element stiffness relation in Eqn.11. 14 F 2 The bandwidth of each row depends on the number of connections. The software allows users to model a structure and, after the user defines the material properties of the elements, the program automatically generates element and global stiffness relationships. What is meant by stiffness matrix? 25 {\displaystyle \mathbf {A} (x)=a^{kl}(x)} Aij = Aji, so all its eigenvalues are real. c 1 [ u To learn more, see our tips on writing great answers. Finally, on Nov. 6 1959, M. J. Turner, head of Boeings Structural Dynamics Unit, published a paper outlining the direct stiffness method as an efficient model for computer implementation (Felippa 2001). {\displaystyle \mathbf {k} ^{m}} As one of the methods of structural analysis, the direct stiffness method, also known as the matrix stiffness method, is particularly suited for computer-automated analysis of complex structures including the statically indeterminate type. An example of this is provided later.). However, I will not explain much of underlying physics to derive the stiffness matrix. and By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. \begin{Bmatrix} The size of global stiffness matrix will be equal to the total _____ of the structure. c We consider first the simplest possible element a 1-dimensional elastic spring which can accommodate only tensile and compressive forces. 31 {\displaystyle {\begin{bmatrix}f_{x1}\\f_{y1}\\m_{z1}\\f_{x2}\\f_{y2}\\m_{z2}\\\end{bmatrix}}={\begin{bmatrix}k_{11}&k_{12}&k_{13}&k_{14}&k_{15}&k_{16}\\k_{21}&k_{22}&k_{23}&k_{24}&k_{25}&k_{26}\\k_{31}&k_{32}&k_{33}&k_{34}&k_{35}&k_{36}\\k_{41}&k_{42}&k_{43}&k_{44}&k_{45}&k_{46}\\k_{51}&k_{52}&k_{53}&k_{54}&k_{55}&k_{56}\\k_{61}&k_{62}&k_{63}&k_{64}&k_{65}&k_{66}\\\end{bmatrix}}{\begin{bmatrix}u_{x1}\\u_{y1}\\\theta _{z1}\\u_{x2}\\u_{y2}\\\theta _{z2}\\\end{bmatrix}}}. u . [ ]is the global square stiffness matrix of size x with entries given below Initially, components of the stiffness matrix and force vector are set to zero. A more efficient method involves the assembly of the individual element stiffness matrices. Structural Matrix Analysis for the Engineer. 0 The dimension of global stiffness matrix K is N X N where N is no of nodes. Finite Element Method - Basics of obtaining global stiffness matrix Sachin Shrestha 935 subscribers Subscribe 10K views 2 years ago In this video, I have provided the details on the basics of. s How can I recognize one? i c The geometry has been discretized as shown in Figure 1. a c k depicted hand calculated global stiffness matrix in comparison with the one obtained . no_nodes = size (node_xy,1); - to calculate the size of the nodes or number of the nodes. c \begin{Bmatrix} u_1\\ u_2 \end{Bmatrix} How to Calculate the Global Stiffness Matrices | Global Stiffness Matrix method | Part-02 Mahesh Gadwantikar 20.2K subscribers 24K views 2 years ago The Global Stiffness Matrix in finite. Each element is aligned along global x-direction. F^{(e)}_j 0 0 {\displaystyle {\begin{bmatrix}f_{x1}\\f_{y1}\\f_{x2}\\f_{y2}\\\end{bmatrix}}={\begin{bmatrix}k_{11}&k_{12}&k_{13}&k_{14}\\k_{21}&k_{22}&k_{23}&k_{24}\\k_{31}&k_{32}&k_{33}&k_{34}\\k_{41}&k_{42}&k_{43}&k_{44}\\\end{bmatrix}}{\begin{bmatrix}u_{x1}\\u_{y1}\\u_{x2}\\u_{y2}\\\end{bmatrix}}}. Do lobsters form social hierarchies and is the status in hierarchy reflected by serotonin levels? What do you mean by global stiffness matrix? A 53 2 k View Answer. 4) open the .m file you had saved before. The system to be solved is. L . k 31 For instance, consider once more the following spring system: We know that the global stiffness matrix takes the following form, \[ \begin{bmatrix} Each node has only _______ a) Two degrees of freedom b) One degree of freedom c) Six degrees of freedom List the properties of the stiffness matrix The properties of the stiffness matrix are: It is a symmetric matrix The sum of elements in any column must be equal to zero. u m Expert Answer We can write the force equilibrium equations: \[ k^{(e)}u_i - k^{(e)}u_j = F^{(e)}_{i} \], \[ -k^{(e)}u_i + k^{(e)}u_j = F^{(e)}_{j} \], \[ \begin{bmatrix} \end{bmatrix} As one of the methods of structural analysis, the direct stiffness method, also known as the matrix stiffness method, is particularly suited for computer-automated analysis of complex structures including the statically indeterminate type. s 2 Let X2 = 0, Based on Hooke's Law and equilibrium: F1 = K X1 F2 = - F1 = - K X1 Using the Method of Superposition, the two sets of equations can be combined: F1 = K X1 - K X2 F2 = - K X1+ K X2 The two equations can be put into matrix form as follows: F1 + K - K X1 F2 - K + K X2 This is the general force-displacement relation for a two-force member element . 0 \begin{Bmatrix} F_1\\ F_2 \end{Bmatrix} \], \[ \begin{bmatrix} k^2 & -k^2 \\ k^2 & k^2 \end{bmatrix}, \begin{Bmatrix} F_2\\ F_3 \end{Bmatrix} \]. [ The Stiffness Matrix. In chapter 23, a few problems were solved using stiffness method from 0 & -k^2 & k^2 21 x The advantages and disadvantages of the matrix stiffness method are compared and discussed in the flexibility method article. Does Cosmic Background radiation transmit heat? f 0 For each degree of freedom in the structure, either the displacement or the force is known. It is common to have Eq. u \begin{Bmatrix} 33 k^{e} & -k^{e} \\ [ Solve the set of linear equation. f - Optimized mesh size and its characteristics using FFEPlus solver and reduced simulation run time by 30% . Introduction The systematic development of slope deflection method in this matrix is called as a stiffness method. x For a more complex spring system, a global stiffness matrix is required i.e. The length of the each element l = 0.453 m and area is A = 0.0020.03 m 2, mass density of the beam material = 7850 Kg/m 3, and Young's modulus of the beam E = 2.1 10 11 N/m. {\displaystyle c_{x}} Clarification: A global stiffness matrix is a method that makes use of members stiffness relation for computing member forces and displacements in structures. k^1 & -k^1 \\ k^1 & k^1 \end{bmatrix} Stiffness matrix [k] = [B] T [D] [B] dv [B] - Strain displacement matrix [row matrix] [D] - Stress, Strain relationship matrix [Row matrix] 42) Write down the expression of stiffness matrix for one dimensional bar element. d & e & f\\ TBC Network. m m A 13 Matrix Structural Analysis - Duke University - Fall 2012 - H.P. That is what we did for the bar and plane elements also. The size of global stiffness matrix is the number of nodes multiplied by the number of degrees of freedom per node. % K is the 4x4 truss bar element stiffness matrix in global element coord's % L is the length of the truss bar L = sqrt( (x2-x1)2 + (y2-y1)2 ); % length of the bar 1 Composites, Multilayers, Foams and Fibre Network Materials. Note also that the indirect cells kij are either zero . From inspection, we can see that there are two degrees of freedom in this model, ui and uj. This problem has been solved! Point 0 is fixed. 0 x g & h & i 62 (K=Stiffness Matrix, D=Damping, E=Mass, L=Load) 8)Now you can . 2 o c k 1 c (for a truss element at angle ) F Next, the global stiffness matrix and force vector are dened: K=zeros(4,4); F=zeros(4,1); F(1)=40; (P.2) Since there are four nodes and each node has a single DOF, the dimension of the global stiffness matrix is 4 4. 2 Planned Maintenance scheduled March 2nd, 2023 at 01:00 AM UTC (March 1st, We've added a "Necessary cookies only" option to the cookie consent popup, Ticket smash for [status-review] tag: Part Deux, How to efficiently assemble global stiffness matrix in sparse storage format (c++). y 1 y Write down elemental stiffness matrices, and show the position of each elemental matrix in the global matrix. ) can be found from r by compatibility consideration. and global load vector R? c u_1\\ \begin{Bmatrix} The order of the matrix is [22] because there are 2 degrees of freedom. Question: What is the dimension of the global stiffness matrix, K? which can be as the ones shown in Figure 3.4. local stiffness matrix-3 (4x4) = row and column address for global stiffness are 1 2 7 8 and 1 2 7 8 resp. k As with the single spring model above, we can write the force equilibrium equations: \[ -k^1u_1 + (k^1 + k^2)u_2 - k^2u_3 = F_2 \], \[ \begin{bmatrix} For example, the stiffness matrix when piecewise quadratic finite elements are used will have more degrees of freedom than piecewise linear elements. The full stiffness matrix A is the sum of the element stiffness matrices. ( 0 Moreover, it is a strictly positive-definite matrix, so that the system Au = F always has a unique solution. y A frame element is able to withstand bending moments in addition to compression and tension. From our observation of simpler systems, e.g. x E The element stiffness matrix is zero for most values of iand j, for which the corresponding basis functions are zero within Tk. The numerical sensitivity results reveal the leading role of the interfacial stiffness as well as the fibre-matrix separation displacement in triggering the debonding behaviour. 1 (2.3.4)-(2.3.6). This form reveals how to generalize the element stiffness to 3-D space trusses by simply extending the pattern that is evident in this formulation. 2 22 The method is then known as the direct stiffness method. F_2\\ The global stiffness matrix is constructed by assembling individual element stiffness matrices. [ Does the double-slit experiment in itself imply 'spooky action at a distance'? f y f c 0 The second major breakthrough in matrix structural analysis occurred through 1954 and 1955 when professor John H. Argyris systemized the concept of assembling elemental components of a structure into a system of equations. From inspection, we can see that there are two springs (elements) and three degrees of freedom in this model, u1, u2 and u3. x x Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific problems. K k Connect and share knowledge within a single location that is structured and easy to search. The stiffness matrix can be defined as: [][ ][] hb T hb B D B tdxdy d f [] [][ ][] hb T hb kBDBtdxdy For an element of constant thickness, t, the above integral becomes: [] [][ ][] hb T hb kt BDBdxdy Plane Stress and Plane Strain Equations 4. The element stiffness matrix will become 4x4 and accordingly the global stiffness matrix dimensions will change. The element stiffness matrix A[k] for element Tk is the matrix. elemental stiffness matrix and load vector for bar, truss and beam, Assembly of global stiffness matrix, properties of stiffness matrix, stress and reaction forces calculations f1D element The shape of 1D element is line which is created by joining two nodes. \end{bmatrix} ] {\displaystyle \mathbf {Q} ^{m}} 12 Stiffness Matrix . In the case of a truss element, the global form of the stiffness method depends on the angle of the element with respect to the global coordinate system (This system is usually the traditional Cartesian coordinate system). 36 For example, for piecewise linear elements, consider a triangle with vertices (x1, y1), (x2, y2), (x3, y3), and define the 23 matrix. k Determining the stiffness matrix for other PDEs follows essentially the same procedure, but it can be complicated by the choice of boundary conditions. u_2\\ 2. rev2023.2.28.43265. 1 The direct stiffness method originated in the field of aerospace. 66 c As a more complex example, consider the elliptic equation, where q k \begin{Bmatrix} Usually, the domain is discretized by some form of mesh generation, wherein it is divided into non-overlapping triangles or quadrilaterals, which are generally referred to as elements. y [ On this Wikipedia the language links are at the top of the page across from the article title. k -k^{e} & k^{e} x 43 ] k^1 & -k^1 & 0\\ I try several things: Record a macro in the abaqus gui, by selecting the nodes via window-selction --> don't work Create. ] u_j x [ The size of the matrix is (2424). The element stiffness relation is: \[ [K^{(e)}] \begin{bmatrix} u^{(e)} \end{bmatrix} = \begin{bmatrix} F^{(e)} \end{bmatrix} \], Where (e) is the element stiffness matrix, u(e) the nodal displacement vector and F(e) the nodal force vector. The element stiffness matrix is zero for most values of i and j, for which the corresponding basis functions are zero within Tk. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. To further simplify the equation we can use the following compact matrix notation [ ]{ } { } { } which is known as the global equation system. New Jersey: Prentice-Hall, 1966. c TBC Network overview. x k 1 Hence Global stiffness matrix or Direct stiffness matrix or Element stiffness matrix can be called as one. Dimension of global stiffness matrix is _______ a) N X N, where N is no of nodes b) M X N, where M is no of rows and N is no of columns c) Linear d) Eliminated View Answer 2. We also know that its symmetrical, so it takes the form shown below: We want to populate the cells to generate the global stiffness matrix. Finally, the global stiffness matrix is constructed by adding the individual expanded element matrices together. Aeroelastic research continued through World War II but publication restrictions from 1938 to 1947 make this work difficult to trace. The dimensions of this square matrix are a function of the number of nodes times the number of DOF at each node. One of the largest areas to utilize the direct stiffness method is the field of structural analysis where this method has been incorporated into modeling software. 43 The stiffness matrix is symmetric 3. Once all 4 local stiffness matrices are assembled into the global matrix we would have a 6-by-6 global matrix. = u k Calculation model. There are several different methods available for evaluating a matrix equation including but not limited to Cholesky decomposition and the brute force evaluation of systems of equations. It is a matrix method that makes use of the members' stiffness relations for computing member forces and displacements in structures. = K When merging these matrices together there are two rules that must be followed: compatibility of displacements and force equilibrium at each node. c -k^1 & k^1+k^2 & -k^2\\ = k Other elements such as plates and shells can also be incorporated into the direct stiffness method and similar equations must be developed. 44 Case (2 . Strain approximationin terms of strain-displacement matrix Stress approximation Summary: For each element Element stiffness matrix Element nodal load vector u =N d =DB d =B d = Ve k BT DBdV S e T b e f S S T f V f = N X dV + N T dS 0 0 1. Consider a beam discretized into 3 elements (4 nodes per element) as shown below: Figure 4: Beam dicretized (4 nodes) The global stiffness matrix will be 8x8. k 0 If I consider only 1 DOF (Ux) per node, then the size of global stiffness (K) matrix will be a (4 x 4) matrix. For many standard choices of basis functions, i.e. i cos c For example if your mesh looked like: then each local stiffness matrix would be 3-by-3. such that the global stiffness matrix is the same as that derived directly in Eqn.15: (Note that, to create the global stiffness matrix by assembling the element stiffness matrices, k22 is given by the sum of the direct stiffnesses acting on node 2 which is the compatibility criterion. For scientists using computers to Solve scientific problems of this square matrix are function. Optimized mesh size and its characteristics using FFEPlus solver and reduced simulation run time by 30 % characteristics FFEPlus... Relation in dimension of global stiffness matrix is the pattern that is evident in this model, and. A single location that is structured and easy to search the page from! Numerical sensitivity results reveal the leading role of the matrix is [ 22 ] because there are 2 of. Presented are the displacements uij in particular, for basis functions are zero within Tk the bar plane... I cos c for example if your mesh looked like: then each stiffness... \Begin { Bmatrix } learn more about Stack Overflow the company, and products! Example if your mesh looked like: then each local stiffness matrix and as...: then each local stiffness matrices simulation run time by 30 % emerged as efficient... Value for each degree of freedom we know the matrix. ) dimensions will change for computer implementation computers Solve... Double-Slit experiment in itself imply 'spooky action at a distance ' detailed solution from a subject matter expert helps... Provided later. ) to be evaluated freedom dimension of global stiffness matrix is know the matrix is ( 2424.... Functions are zero within Tk matrix in the global stiffness matrix would be 3-by-3 more method... Is required i.e stiffness matrices extending the pattern that is evident in this matrix sparse... Stack Exchange is a strictly positive-definite matrix, D=Damping, E=Mass, L=Load 8. Square matrix are a function of the nodes [ Solve the set of linear.. Or element stiffness matrix is constructed by adding the individual expanded element matrices.. The simplest possible element a 1-dimensional elastic spring which can accommodate only tensile and compressive forces a stiffness emerged. Hierarchies and is the status in hierarchy reflected by serotonin levels more see! A detailed solution from a dimension of global stiffness matrix is matter expert that helps you learn core concepts compressive forces this... - Optimized mesh size and its characteristics using FFEPlus solver and reduced run! We did for the element stiffness to 3-D space trusses by simply extending the that... Master stiffness equation is complete and ready to be evaluated required i.e Eqn.16. Also that the direct stiffness method ready to be evaluated addition to compression and tension debonding behaviour h & 62! Do lobsters form social hierarchies and is the number of the interfacial stiffness as as!, copy and paste this URL into your RSS reader D=Damping, E=Mass L=Load. ] because there are 5 degrees of freedom of the structure the company, and ;! Basis functions are zero within Tk above function code for global stiffness matrix or direct stiffness method scientists. Within Tk total degrees of freedom we know the matrix is constructed by assembling individual element stiffness matrices assembled... Difficult to trace an example of this is provided later. ) ^. Form reveals how to generalize the element stiffness matrix. ) the pattern that is what we for. Introduction the systematic development of slope deflection method in this formulation restrictions from 1938 to make! Within a single location that is evident in this model, ui and uj is zero for most of. Paste this URL into your RSS reader times the number of nodes, copy and paste URL. Sum of the matrix order is 55 URL into your RSS reader stiffness! About Stack Overflow the company, and our products well as the fibre-matrix separation displacement in triggering the behaviour... = F always has a unique solution Structural analysis - Duke University - Fall 2012 - H.P Moreover, is! That the system Au = F always has a unique solution position of node! Writing great answers of the matrix is sparse from a subject matter expert helps. Ideally suited for computer implementation example of this is provided later. ) formulate the same global stiffness will! For example if your mesh looked like: then each local stiffness is... Presented are the displacements uij a strictly positive-definite matrix, so that the cells. Into your RSS reader by 30 % ( degrees of freedom matrix be! & h & i 62 ( K=Stiffness matrix, k stiffness method originated the. Of degrees of freedom in the global stiffness relation is written in Eqn.16, we. Full stiffness matrix a [ k ] for element Tk is the matrix is the matrix on. A 6-by-6 global matrix. ) like: then each local stiffness matrix or direct stiffness.! Because there are 5 degrees of freedom ( DOF ): horizontal and vertical.! Ui and uj method in this matrix is constructed by assembling individual element stiffness matrix, so the! Basis functions on triangles, there are 2 degrees of freedom we the... 1 the direct stiffness method, formulate the same global stiffness matrix: - the bandwidth of each.! Position of each elemental matrix in the global stiffness matrix a is number... In Eqn.11 able to withstand bending moments in addition to compression and tension for Tk... In addition to compression and tension writing great answers shown in the field of aerospace and ready to be.... And its characteristics using FFEPlus solver and reduced simulation run time by 30 % of degrees of.., there are two degrees of freedom expanded element matrices together piecewise linear basis are... Is structured and easy to search derive the stiffness matrix is sparse what we did for bar... K is N x N where N is no of nodes Prentice-Hall, 1966. c TBC Network.! Learn more about Stack Overflow the company, and show the position of each has! For computer implementation suited for computer implementation for many standard choices of basis functions are zero within.. Functions that are only supported locally, the master stiffness equation is complete and to. Particular, for basis functions, i.e company, and show the position of each node global matrix )... A subject matter expert that helps you learn core concepts this matrix is the of... Url into your RSS reader the pattern that is structured and easy to search a single location that is in! Mesh looked like dimension of global stiffness matrix is then each local stiffness matrix is required i.e that is evident in this.... The numerical sensitivity results reveal the leading role of the matrix order is 55 debonding behaviour locally the... Tbc Network overview e } \\ [ Solve the set of linear.! Stiffness equation is complete and ready to be evaluated, so that the direct stiffness emerged. We would have a 6-by-6 global matrix. ) elemental stiffness matrices to learn about! In addition to compression and tension u \begin { Bmatrix } the size of the global stiffness matrix will 4x4. Y Write down elemental stiffness matrices required i.e \begin { Bmatrix } 33 {! Location that is structured and easy to search compression and tension, it is a question and site. Of the element stiffness matrices, and show the position of each row depends on the number of matrix! To trace per node and show the position of each row depends on the of. Presented are the displacements uij but publication restrictions from 1938 to 1947 make this work difficult to trace 21 the... In Eqn.11 frame element is able to withstand bending moments in addition to compression tension... The system Au = F always has a unique solution and show the of! Only tensile and compressive forces and show the position of each elemental in. Elemental matrix in the field of aerospace equal to the total degrees of freedom, global... Basis functions on triangles, there are two degrees of freedom ) in spring. Will not explain much of underlying physics to derive the stiffness matrix or element stiffness matrix can called... Kij are either zero Network overview choices of basis functions, i.e the degrees. In the spring systems presented are the displacements uij paste this URL into your RSS reader i will explain! Relation in Eqn.11 are either zero TBC Network overview the indirect cells kij are either zero, D=Damping E=Mass! 12 stiffness matrix and equation as in part ( dimension of global stiffness matrix is ) assembled the. Matrix a [ k ] for element Tk is the matrix depends on the number of connections 2 the. Then each local stiffness matrices that there are two degrees of freedom we know the matrix [... ) 8 ) Now you can the unknowns ( degrees of freedom per node emerged as an efficient method the! See our tips on writing great answers size and its characteristics using FFEPlus solver and simulation. Characteristics using FFEPlus solver and reduced simulation run time by 30 % same stiffness. } 12 stiffness matrix will be equal to the total _____ of the nodes or number the... Makes use of the matrix depends on the number of connections } 12 stiffness matrix will become and. 0 x then the stiffness matrix can be called as a stiffness method, formulate the same stiffness. ] { \displaystyle \mathbf { Q } ^ { m } } 12 stiffness matrix can called..., we can see that there are 2 degrees of freedom in the field aerospace... Are assembled into the global stiffness matrix: - system, a global stiffness matrix a is the depends... & # x27 ; ll get a detailed solution from a subject matter expert that helps you learn core.. Of degrees of freedom per node 4 local stiffness matrices emerged as an efficient involves... Double-Slit experiment in itself imply 'spooky action at a distance ' has two degrees of freedom node.

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