{"history":[],"article":{"id":"9375b199-3916-4b46-bcdc-e322495364d5","title":"Bending of plates","slug":"bending-of-plates","content":":::summary\n:::\n\n# \n**Bending of [plate](https://bliptext.com/articles/plate-metal)s**, or **[plate](https://bliptext.com/articles/plate-metal) bending**, refers to the [deflection](https://bliptext.com/articles/deflection-engineering) of a [plate](https://bliptext.com/articles/plate-metal) perpendicular to the plane of the [plate](https://bliptext.com/articles/plate-metal) under the action of external [forces](https://bliptext.com/articles/force) and [moments](https://bliptext.com/articles/moment-physics).\nThe amount of deflection can be determined by solving the differential equations of an appropriate [plate theory](https://bliptext.com/articles/plate-theory).\nThe [stresses](https://bliptext.com/articles/stress-physics) in the plate can be calculated from these deflections.\nOnce the stresses are known, [failure theories](https://bliptext.com/articles/material-failure-theory) can be used to determine whether a plate will fail under a given load.\n# [Bending of an edge-clamped circular plate under the action of a transverse pressure. The left half of the plate shows the deformed shape, while the right half shows the undeformed shape. This calculation was performed using Ansys. | upload.wikimedia.org/wikipedia/commons/8/85/BendingCircularPlate.png]\n\n# Bending of Kirchhoff-Love plates\n# [Forces and moments on a flat plate. | upload.wikimedia.org/wikipedia/commons/e/eb/PlateForcesMoments///upd.png]\n\n## Definitions\nFor a thin rectangular plate of thickness H, [Young's modulus](https://bliptext.com/articles/young-s-modulus) E, and [Poisson's ratio](https://bliptext.com/articles/poisson-s-ratio) \\nu, we can define parameters in terms of the plate deflection, w.\nThe [flexural rigidity](https://bliptext.com/articles/flexural-rigidity) is given by\n\n### Moments\nThe [bending moments](https://bliptext.com/articles/bending-moment) per unit length are given by\nThe [twisting moment](https://bliptext.com/articles/torque) per unit length is given by\n\n### Forces\nThe [shear forces](https://bliptext.com/articles/shear-force) per unit length are given by\n\n### Stresses\nThe bending [stresses](https://bliptext.com/articles/stress-mechanics) are given by The [shear stress](https://bliptext.com/articles/shear-stress) is given by\n\n### Strains\nThe [bending strains](https://bliptext.com/articles/deformation-mechanics) for small-deflection theory are given by\nThe [shear strain](https://bliptext.com/articles/deformation-mechanics) for small-deflection theory is given by\nFor large-deflection plate theory, we consider the inclusion of membrane strains\n\n### Deflections\nThe [deflections](https://bliptext.com/articles/deflection-engineering) are given by\n\n## Derivation\nIn the [Kirchhoff–Love plate theory](https://bliptext.com/articles/kirchhoff-love-plate-theory) for plates the governing equations are\nand\nIn expanded form,\nand\nwhere q(x) is an applied transverse [load](https://bliptext.com/articles/structural-load) per unit area, the thickness of the plate is H=2h, the stresses are \\sigma_{ij}, and\nThe quantity N has units of [force](https://bliptext.com/articles/force) per unit length.\nThe quantity M has units of [moment](https://bliptext.com/articles/moment-physics) per unit length.\nFor [isotropic](https://bliptext.com/articles/isotropic), [homogeneous](https://bliptext.com/articles/homogeneous), plates with [Young's modulus](https://bliptext.com/articles/young-s-modulus) E and [Poisson's ratio](https://bliptext.com/articles/poisson-s-ratio) \\nu these equations reduce to where w(x_1,x_2) is the deflection of the mid-surface of the plate.\n\n## Small deflection of thin rectangular plates\nThis is governed by the [Germain](https://bliptext.com/articles/sophie-germain)-[Lagrange](https://bliptext.com/articles/joseph-louis-lagrange) plate equation\nThis equation was first derived by Lagrange in December 1811 in correcting the work of Germain who provided the basis of the theory.\n\n## Large deflection of thin rectangular plates\nThis is governed by the [Föppl](https://bliptext.com/articles/august-f-ppl)–[von Kármán](https://bliptext.com/articles/theodore-von-k-rm-n) [plate equations](https://bliptext.com/articles/f-ppl-von-k-rm-n-equations)\nwhere F is the stress function.\n\n# Circular Kirchhoff-Love plates\nThe bending of circular plates can be examined by solving the governing equation with\nappropriate boundary conditions.\nThese solutions were first found by Poisson in 1829.\nCylindrical coordinates are convenient for such problems.\nHere z is the distance of a point from the midplane of the plate.\nThe governing equation in coordinate-free form is In cylindrical coordinates ,\nFor symmetrically loaded circular plates, w = w(r), and we have\nTherefore, the governing equation is If q and D are constant, direct integration of the governing equation gives us

\nwhere C_i are constants.\nThe slope of the deflection surface is For a circular plate, the requirement that the deflection and the slope of the deflection are finite\nat r = 0 implies that C_1 = 0.\nHowever, C_3 need not equal 0, as the limit\nof r \\ln r\\, exists as you approach r = 0 from the right.\n\n## Clamped edges\nFor a circular plate with clamped edges, we have w(a) = 0 and \\phi(a) = 0 at the edge of the plate (radius a).\nUsing these boundary conditions we get\n
\nThe in-plane displacements in the plate are\nThe in-plane strains in the plate are\nThe in-plane stresses in the plate are\nFor a plate of thickness 2h, the bending stiffness is and we have\n
\nThe moment resultants (bending moments) are\nThe maximum radial stress is at z = h and r = a: where H := 2h.\nThe bending moments at the boundary and the center of the plate are\n\n# Rectangular Kirchhoff-Love plates\nFor rectangular plates, Navier in 1820 introduced a simple method for finding the displacement and stress when a plate is simply supported.\nThe idea was to express the applied load in terms of Fourier components, find the solution for a sinusoidal load (a single Fourier component), and then superimpose the Fourier components to get the solution for an arbitrary load.\n# [Bending of a rectangular plate under the action of a distributed force q per unit area. | upload.wikimedia.org/wikipedia/commons/d/d0/RectangularPlateBending.svg]\n\n## Sinusoidal load\nLet us assume that the load is of the form\nHere q_0 is the amplitude, a is the width of the plate in the x-direction, and\nb is the width of the plate in the y-direction.\nSince the plate is simply supported, the displacement w(x,y) along the edges of the plate is zero, the bending moment M_{xx} is zero at x=0 and x=a, and\nM_{yy} is zero at y=0 and y=b.\nIf we apply these boundary conditions and solve the plate equation, we get the\nsolution\nWhere D is the flexural rigidity\nAnalogous to flexural stiffness EI.\nWe can calculate the stresses and strains in the plate once we know the displacement.\nFor a more general load of the form\nwhere m and n are integers, we get the solution\n
\n\n## Navier solution\n\n### Double trigonometric series equation\nWe define a general load q(x,y) of the following form\nwhere a_{mn} is a Fourier coefficient given by The classical rectangular plate equation for small deflections thus becomes:\n\n### Simply-supported plate with general load\nWe assume a solution w(x,y) of the following form\nThe partial differentials of this function are given by Substituting these expressions in the plate equation, we have\nEquating the two expressions, we have\nwhich can be rearranged to give\nThe deflection of a simply-supported plate (of corner-origin) with general load is given by
\n\n### Simply-supported plate with uniformly-distributed load\nFor a uniformly-distributed load, we have\nThe corresponding Fourier coefficient is thus given by Evaluating the double integral, we have\nor alternatively in a [piecewise](https://bliptext.com/articles/piecewise) format, we have\nThe deflection of a simply-supported plate (of corner-origin) with uniformly-distributed load is given by
\nThe bending moments per unit length in the plate are given by
\n\n## Lévy solution\nAnother approach was proposed by [Lévy](https://bliptext.com/articles/maurice-l-vy) in 1899.\nIn this case we start with an assumed form of the displacement and try to fit the parameters so that the governing equation and the boundary conditions are satisfied.\nThe goal is to find Y_m(y) such that it satisfies the boundary conditions at y = 0 and y = b and, of course, the governing equation.\nLet us assume that\nFor a plate that is simply-supported along x=0 and x=a, the boundary conditions are w=0 and M_{xx}=0.\nNote that there is no variation in displacement along these edges meaning that and, thus reducing the moment boundary condition to an equivalent expression.\n\n### Moments along edges\nConsider the case of pure moment loading.\nIn that case q = 0 and\nw(x,y) has to satisfy.\nSince we are working in rectangular\nCartesian coordinates, the governing equation can be expanded as Plugging the expression for w(x,y) in the governing equation gives us or This is an ordinary differential equation which has the general solution\nwhere are constants that can be determined from the boundary\nconditions.\nTherefore, the displacement solution has the form\n
\nLet us choose the coordinate system such that the boundaries of the plate are\nat x = 0 and x = a (same as before) and at y = \\pm b/2 (and not y=0 and y=b).\nThen the moment boundary conditions at the y = \\pm b/2 boundaries are\nwhere are known functions.\nThe solution can be found by applying these boundary conditions.\nWe can show that for the symmetrical case\nwhere\nand\nwe have\n
\nwhere\nSimilarly, for the antisymmetrical case where\nwe have\n
\nWe can superpose the symmetric and antisymmetric solutions to get more general\nsolutions.\n\n### Simply-supported plate with uniformly-distributed load\nFor a uniformly-distributed load, we have\nThe deflection of a simply-supported plate with centre with uniformly-distributed load is given by
\nThe bending moments per unit length in the plate are given by
\n\n### Uniform and symmetric moment load\nFor the special case where the loading is symmetric and the moment is uniform, we have at y=\\pm b/2,\nThe resulting displacement is
\nwhere\nThe bending moments and shear forces corresponding to the displacement w are\nThe stresses are\n\n## Cylindrical plate bending\nCylindrical bending occurs when a rectangular plate that has dimensions, where a \\ll b and the thickness h is small, is subjected to a uniform distributed load perpendicular to the plane of the plate.\nSuch a plate takes the shape of the surface of a cylinder.\n\n### Simply supported plate with axially fixed ends\nFor a simply supported plate under cylindrical bending with edges that are free to rotate but have a fixed x_1.\nCylindrical bending solutions can be found using the Navier and Levy techniques.\n\n# Bending of thick Mindlin plates\nFor thick plates, we have to consider the effect of through-the-thickness shears on the orientation of the normal to the mid-surface after deformation.\n[Raymond D. Mindlin's](https://bliptext.com/articles/raymond-d-mindlin) theory provides one approach for find the deformation and stresses in such plates.\nSolutions to Mindlin's theory can be derived from the equivalent Kirchhoff-Love solutions using canonical relations.\n\n## Governing equations\nThe canonical governing equation for isotropic thick plates can be expressed as where q is the applied transverse load, G is the shear modulus,\nis the bending rigidity, h is the plate thickness, ,\n\\kappa is the shear correction factor, E is the Young's modulus, \\nu is the Poisson's ratio, and\nIn Mindlin's theory, w is the transverse displacement of the mid-surface of the plate\nand the quantities \\varphi_1 and \\varphi_2 are the rotations of the mid-surface normal\nabout the x_2 and x_1-axes, respectively.\nThe canonical parameters for this theory\nare and.\nThe shear correction factor \\kappa usually has the\nvalue 5/6.\nThe solutions to the governing equations can be found if one knows the corresponding\nKirchhoff-Love solutions by using the relations\nwhere w^K is the displacement predicted for a Kirchhoff-Love plate, \\Phi is a biharmonic function such that, \\Psi is a function that satisfies the\nLaplace equation,, and\n\n## Simply supported rectangular plates\nFor simply supported plates, the Marcus moment sum vanishes, i.e.,\nWhich is almost Laplace`s equation for w[ref 6].\nIn that case the functions \\Phi, \\Psi, \\Omega vanish, and the Mindlin solution is related to the corresponding Kirchhoff solution by\n\n# Bending of Reissner-Stein cantilever plates\nReissner-Stein theory for cantilever plates leads to the following coupled ordinary differential equations for a cantilever plate with concentrated end load q_x(y) at x=a.\nand the boundary conditions at x=a are\nSolution of this system of two ODEs gives\nwhere.\nThe bending moments and shear forces corresponding to the displacement\nare\nThe stresses are\nIf the applied load at the edge is constant, we recover the solutions for a beam under a concentrated end load.\nIf the applied load is a linear function of y, then","current_revision":null,"created_by":"kACnuQmH5k9Nr5VNVEpVeg7XpvUmMctD","created_at":"2025-01-26T12:41:38.472Z","updated_at":"2025-01-26T12:41:38.472Z","search_vector":"'bend':1 'plate':3","search_content":" \n \n\n# \n**Bending of [plate](https://bliptext.com/articles/plate-metal)s**, or **[plate](https://bliptext.com/articles/plate-metal) bending**, refers to the [deflection](https://bliptext.com/articles/deflection-engineering) of a [plate](https://bliptext.com/articles/plate-metal) perpendicular to the plane of the [plate](https://bliptext.com/articles/plate-metal) under the action of external [forces](https://bliptext.com/articles/force) and [moments](https://bliptext.com/articles/moment-physics).\nThe amount of deflection can be determined by solving the differential equations of an appropriate [plate theory](https://bliptext.com/articles/plate-theory).\nThe [stresses](https://bliptext.com/articles/stress-physics) in the plate can be calculated from these deflections.\nOnce the stresses are known, [failure theories](https://bliptext.com/articles/material-failure-theory) can be used to determine whether a plate will fail under a given load.\n# [Bending of an edge-clamped circular plate under the action of a transverse pressure. The left half of the plate shows the deformed shape, while the right half shows the undeformed shape. This calculation was performed using Ansys. | upload.wikimedia.org/wikipedia/commons/8/85/BendingCircularPlate.png]\n\n# Bending of Kirchhoff-Love plates\n# [Forces and moments on a flat plate. | upload.wikimedia.org/wikipedia/commons/e/eb/PlateForcesMoments///upd.png]\n\n## Definitions\nFor a thin rectangular plate of thickness H, [Young's modulus](https://bliptext.com/articles/young-s-modulus) E, and [Poisson's ratio](https://bliptext.com/articles/poisson-s-ratio) \\nu, we can define parameters in terms of the plate deflection, w.\nThe [flexural rigidity](https://bliptext.com/articles/flexural-rigidity) is given by\n\n### Moments\nThe [bending moments](https://bliptext.com/articles/bending-moment) per unit length are given by\nThe [twisting moment](https://bliptext.com/articles/torque) per unit length is given by\n\n### Forces\nThe [shear forces](https://bliptext.com/articles/shear-force) per unit length are given by\n\n### Stresses\nThe bending [stresses](https://bliptext.com/articles/stress-mechanics) are given by The [shear stress](https://bliptext.com/articles/shear-stress) is given by\n\n### Strains\nThe [bending strains](https://bliptext.com/articles/deformation-mechanics) for small-deflection theory are given by\nThe [shear strain](https://bliptext.com/articles/deformation-mechanics) for small-deflection theory is given by\nFor large-deflection plate theory, we consider the inclusion of membrane strains\n\n### Deflections\nThe [deflections](https://bliptext.com/articles/deflection-engineering) are given by\n\n## Derivation\nIn the [Kirchhoff–Love plate theory](https://bliptext.com/articles/kirchhoff-love-plate-theory) for plates the governing equations are\nand\nIn expanded form,\nand\nwhere q(x) is an applied transverse [load](https://bliptext.com/articles/structural-load) per unit area, the thickness of the plate is H=2h, the stresses are \\sigma_{ij}, and\nThe quantity N has units of [force](https://bliptext.com/articles/force) per unit length.\nThe quantity M has units of [moment](https://bliptext.com/articles/moment-physics) per unit length.\nFor [isotropic](https://bliptext.com/articles/isotropic), [homogeneous](https://bliptext.com/articles/homogeneous), plates with [Young's modulus](https://bliptext.com/articles/young-s-modulus) E and [Poisson's ratio](https://bliptext.com/articles/poisson-s-ratio) \\nu these equations reduce to where w(x_1,x_2) is the deflection of the mid-surface of the plate.\n\n## Small deflection of thin rectangular plates\nThis is governed by the [Germain](https://bliptext.com/articles/sophie-germain)-[Lagrange](https://bliptext.com/articles/joseph-louis-lagrange) plate equation\nThis equation was first derived by Lagrange in December 1811 in correcting the work of Germain who provided the basis of the theory.\n\n## Large deflection of thin rectangular plates\nThis is governed by the [Föppl](https://bliptext.com/articles/august-f-ppl)–[von Kármán](https://bliptext.com/articles/theodore-von-k-rm-n) [plate equations](https://bliptext.com/articles/f-ppl-von-k-rm-n-equations)\nwhere F is the stress function.\n\n# Circular Kirchhoff-Love plates\nThe bending of circular plates can be examined by solving the governing equation with\nappropriate boundary conditions.\nThese solutions were first found by Poisson in 1829.\nCylindrical coordinates are convenient for such problems.\nHere z is the distance of a point from the midplane of the plate.\nThe governing equation in coordinate-free form is In cylindrical coordinates ,\nFor symmetrically loaded circular plates, w = w(r), and we have\nTherefore, the governing equation is If q and D are constant, direct integration of the governing equation gives us \nwhere C_i are constants.\nThe slope of the deflection surface is For a circular plate, the requirement that the deflection and the slope of the deflection are finite\nat r = 0 implies that C_1 = 0.\nHowever, C_3 need not equal 0, as the limit\nof r \\ln r\\, exists as you approach r = 0 from the right.\n\n## Clamped edges\nFor a circular plate with clamped edges, we have w(a) = 0 and \\phi(a) = 0 at the edge of the plate (radius a).\nUsing these boundary conditions we get\n \nThe in-plane displacements in the plate are\nThe in-plane strains in the plate are\nThe in-plane stresses in the plate are\nFor a plate of thickness 2h, the bending stiffness is and we have\n \nThe moment resultants (bending moments) are\nThe maximum radial stress is at z = h and r = a: where H := 2h.\nThe bending moments at the boundary and the center of the plate are\n\n# Rectangular Kirchhoff-Love plates\nFor rectangular plates, Navier in 1820 introduced a simple method for finding the displacement and stress when a plate is simply supported.\nThe idea was to express the applied load in terms of Fourier components, find the solution for a sinusoidal load (a single Fourier component), and then superimpose the Fourier components to get the solution for an arbitrary load.\n# [Bending of a rectangular plate under the action of a distributed force q per unit area. | upload.wikimedia.org/wikipedia/commons/d/d0/RectangularPlateBending.svg]\n\n## Sinusoidal load\nLet us assume that the load is of the form\nHere q_0 is the amplitude, a is the width of the plate in the x-direction, and\nb is the width of the plate in the y-direction.\nSince the plate is simply supported, the displacement w(x,y) along the edges of the plate is zero, the bending moment M_{xx} is zero at x=0 and x=a, and\nM_{yy} is zero at y=0 and y=b.\nIf we apply these boundary conditions and solve the plate equation, we get the\nsolution\nWhere D is the flexural rigidity\nAnalogous to flexural stiffness EI.\nWe can calculate the stresses and strains in the plate once we know the displacement.\nFor a more general load of the form\nwhere m and n are integers, we get the solution\n \n\n## Navier solution\n\n### Double trigonometric series equation\nWe define a general load q(x,y) of the following form\nwhere a_{mn} is a Fourier coefficient given by The classical rectangular plate equation for small deflections thus becomes:\n\n### Simply-supported plate with general load\nWe assume a solution w(x,y) of the following form\nThe partial differentials of this function are given by Substituting these expressions in the plate equation, we have\nEquating the two expressions, we have\nwhich can be rearranged to give\nThe deflection of a simply-supported plate (of corner-origin) with general load is given by \n\n### Simply-supported plate with uniformly-distributed load\nFor a uniformly-distributed load, we have\nThe corresponding Fourier coefficient is thus given by Evaluating the double integral, we have\nor alternatively in a [piecewise](https://bliptext.com/articles/piecewise) format, we have\nThe deflection of a simply-supported plate (of corner-origin) with uniformly-distributed load is given by \nThe bending moments per unit length in the plate are given by \n\n## Lévy solution\nAnother approach was proposed by [Lévy](https://bliptext.com/articles/maurice-l-vy) in 1899.\nIn this case we start with an assumed form of the displacement and try to fit the parameters so that the governing equation and the boundary conditions are satisfied.\nThe goal is to find Y_m(y) such that it satisfies the boundary conditions at y = 0 and y = b and, of course, the governing equation.\nLet us assume that\nFor a plate that is simply-supported along x=0 and x=a, the boundary conditions are w=0 and M_{xx}=0.\nNote that there is no variation in displacement along these edges meaning that and, thus reducing the moment boundary condition to an equivalent expression.\n\n### Moments along edges\nConsider the case of pure moment loading.\nIn that case q = 0 and\nw(x,y) has to satisfy.\nSince we are working in rectangular\nCartesian coordinates, the governing equation can be expanded as Plugging the expression for w(x,y) in the governing equation gives us or This is an ordinary differential equation which has the general solution\nwhere are constants that can be determined from the boundary\nconditions.\nTherefore, the displacement solution has the form\n \nLet us choose the coordinate system such that the boundaries of the plate are\nat x = 0 and x = a (same as before) and at y = \\pm b/2 (and not y=0 and y=b).\nThen the moment boundary conditions at the y = \\pm b/2 boundaries are\nwhere are known functions.\nThe solution can be found by applying these boundary conditions.\nWe can show that for the symmetrical case\nwhere\nand\nwe have\n \nwhere\nSimilarly, for the antisymmetrical case where\nwe have\n \nWe can superpose the symmetric and antisymmetric solutions to get more general\nsolutions.\n\n### Simply-supported plate with uniformly-distributed load\nFor a uniformly-distributed load, we have\nThe deflection of a simply-supported plate with centre with uniformly-distributed load is given by \nThe bending moments per unit length in the plate are given by \n\n### Uniform and symmetric moment load\nFor the special case where the loading is symmetric and the moment is uniform, we have at y=\\pm b/2,\nThe resulting displacement is \nwhere\nThe bending moments and shear forces corresponding to the displacement w are\nThe stresses are\n\n## Cylindrical plate bending\nCylindrical bending occurs when a rectangular plate that has dimensions, where a \\ll b and the thickness h is small, is subjected to a uniform distributed load perpendicular to the plane of the plate.\nSuch a plate takes the shape of the surface of a cylinder.\n\n### Simply supported plate with axially fixed ends\nFor a simply supported plate under cylindrical bending with edges that are free to rotate but have a fixed x_1.\nCylindrical bending solutions can be found using the Navier and Levy techniques.\n\n# Bending of thick Mindlin plates\nFor thick plates, we have to consider the effect of through-the-thickness shears on the orientation of the normal to the mid-surface after deformation.\n[Raymond D. Mindlin's](https://bliptext.com/articles/raymond-d-mindlin) theory provides one approach for find the deformation and stresses in such plates.\nSolutions to Mindlin's theory can be derived from the equivalent Kirchhoff-Love solutions using canonical relations.\n\n## Governing equations\nThe canonical governing equation for isotropic thick plates can be expressed as where q is the applied transverse load, G is the shear modulus,\nis the bending rigidity, h is the plate thickness, ,\n\\kappa is the shear correction factor, E is the Young's modulus, \\nu is the Poisson's ratio, and\nIn Mindlin's theory, w is the transverse displacement of the mid-surface of the plate\nand the quantities \\varphi_1 and \\varphi_2 are the rotations of the mid-surface normal\nabout the x_2 and x_1-axes, respectively.\nThe canonical parameters for this theory\nare and.\nThe shear correction factor \\kappa usually has the\nvalue 5/6.\nThe solutions to the governing equations can be found if one knows the corresponding\nKirchhoff-Love solutions by using the relations\nwhere w^K is the displacement predicted for a Kirchhoff-Love plate, \\Phi is a biharmonic function such that, \\Psi is a function that satisfies the\nLaplace equation,, and\n\n## Simply supported rectangular plates\nFor simply supported plates, the Marcus moment sum vanishes, i.e.,\nWhich is almost Laplace`s equation for w[ref 6].\nIn that case the functions \\Phi, \\Psi, \\Omega vanish, and the Mindlin solution is related to the corresponding Kirchhoff solution by\n\n# Bending of Reissner-Stein cantilever plates\nReissner-Stein theory for cantilever plates leads to the following coupled ordinary differential equations for a cantilever plate with concentrated end load q_x(y) at x=a.\nand the boundary conditions at x=a are\nSolution of this system of two ODEs gives\nwhere.\nThe bending moments and shear forces corresponding to the displacement\nare\nThe stresses are\nIf the applied load at the edge is constant, we recover the solutions for a beam under a concentrated end load.\nIf the applied load is a linear function of y, then","revisionCount":0},"hasMore":false,"nextCursor":null}

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