Geometric non-linearity

Large displacements in truss elements:

• the unrotated element (1)
  
• limit point behaviour with one variable (2)
  
• hardening with one variable (3)
  
• bifurcation problem (4)
  
• limit point with two variables (5)
  
• hardening with two variables (6)
  
• snap back (7)
  

Available From:

• P03
  
  
• R0065 (subset of above): 

  Background to Finite Element Analysis of Geometric Nonlinearity

  
  
  
• R0080 (subset of above): 

  Understanding Nonlinear Finite Element Analysis Through Illustrative Benchmarks

  
  
  

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Large displacements and rotations in thin 2D beams and axisymmetric shells:

• rigid body rotation (NLGB1)
  
• straight cantilever with end moment (NLGB2)
  
• curved cantilever with end moment (NLGB3)
  
• straight cantilever with transverse free end point load (NLGB4)
  
• straight cantilever with axial free end point load (NLGB5)
  
• symmetric shallow pinned arch buckling (NLGB6)
  
• unsymmetric deep arch buckling (NLGB7)
  
• Lee’s frame buckling problem (NLGB8)
  
• built-in circular plate with uniformly distributed load (NLGS1)
  
• annular plate with inside edge load (NLGS2)
  
• truncated cone with outside edge load (NLGS3)
  
• built-in spherical cap with central point load (NLGS4)
  

Available From

• P10: 

  Finite Element Benchmarks For 2D Beams And Axisymmetric Shells Involving Geometric Non-Linearity

  
  
  
• R0010
  
  
• R0065 (subset of above):

  Background to Finite Element Analysis of Geometric Nonlinearity

  
  
  
• R0080 (subset of above): 

  Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks

  
  
  

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Assembly tests for 3D beams and shells:

• elastic large deflection response of a Z-shaped cantilever beam under end load (3DNLG-1)
  
• elastic large deflection response of a pear shaped cylinder under end shortening (3DNLG-2)
  
• elastic lateral buckling of a right angle frame under in-plane end moments (3DNLG-3)
  
• lateral-torsional buckling of an elastic cantilever subjected to a transverse follower force (3DNLG-4)
  
• large deflection of a curved elastic cantilever under transverse end load (3DNLG-5)
  
• buckling of a flat plate with an initial imperfection when subjected to in-plane shear (3DNLG-6)
  
• large deflection elastic response of a hinged spherical shell with uniform pressure loading (3DNLG-7)
  
• collapse of a straight pipe under pure bending (3DNLG-8)
  
• large elastic deflection of a pinched hemispherical shell (3DNLG-8)
  
• elasto-plastic behaviour of a stiffened cylindrical shell panel under compressive end load (3DNLG-10)
  

Available From

• R0024: Assembly Benchmark Tests for 3D Beams & Shell Exhibiting Geometric Non-Linear Behaviour (Summary)

• R0029: 

  Assembly Benchmark Tests For 3D Beams & Shell Exhibiting Geometric Non-Linear Behaviour

  
  
  
• R0065 (subset of above)

  Background to Finite Element Analysis of Geometric Nonlinearity
  
  

• R0080 (subset of above) 

  Understanding Nonlinear Finite Element Analysis Through Illustrative Benchmarks

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A survey of possible benchmarks for 3D beams:

• elastic lateral-torsional buckling of a cantilever (B1)
  
• elastic lateral buckling of a right angle frame under in-plane end moments (B2)
  
• lateral buckling of an I-beam cantilever subjected to transverse force (B3)
  
• elastic circular ring subjected to non-uniform pressure (B4)
  
• elastic large deflection of a cantilever under follower transverse force (B5)
  
• elasto-plastic large deflection of a cantilever under transverse end load (B6)
  
• elastic large deflection of pinned deep arch subjected to central load(B7)
  
• elastic large deflection of cantilever 450 bend subject to end load (B8)
  
• elastic large deflection analysis of a prestressed cable (B9)
  
• elastic large deflection behaviour of a cable under gravity load (B10)
• torsional buckling of end loaded cantilever (B11)
• elastic large deflection behaviour of Lee’s frame (B12)
  
• elastic large deflection of curved beam under non-conservative in-plane load (B13)
  
• clamped-hinged deep circular arch subjected to a point load (B14)
  
• large deflection of a diamond shaped frame (B15)
  
• planar square frame loaded at the midpoints on opposite sides (B16)
  
• cantilever under end moment (B17)
  
• large deflection of a cantilever right angle frame under end load (B18)
  
• elasto-plastic collapse of a 900 pipe bend (B19)
  
• elasto-plastic collapse of a thin walled elbow under in-plane loading and internal pressure (B20)
  
• uniform collapse of a curved pipe under pure bending and internal pressure (B21)
  
• elasto-plastic large deflection response of a Z-shaped cantilever beam (B22)
  
• elasto-plastic analysis of I beams in torsion (B23)
  
• finite rigid body rotation of a curved arch (B24)
  
• collapse analysis of elasto-perfectly plastic triangular truss structure (B25)
  
• elasto-plastic large deformation of a clamped beam under point load (B26)
  
• plastic collapse of a two bay two story frame (B27)
  

Available From

• R0009
  

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A survey of possible benchmarks for 3D shells:

• elastic large deflection response of a centrally loaded spherical shell (S1)
  
• large deflection elastoplastic analysis of a cylindrical shell roof (S2)
  
• thermal buckling of a simply supported rectangular plate (S3)
  
• elastic post-buckling behaviour of a square plate subjected to shear (S4)
  
• elastic large deflection of a cantilever plate with end moment (S5)
  
• elastoplastic buckling of a clamped imperfect spherical cap subjected to uniform pressure (S6)
  
• elastic large deflection analysis of a pinched hemispherical shell (S7)
  
• elastic large deflection of a hyperbolic paraboloid under concentrated moment at corners (S8)
  
• elastic large deflection of a cylindrical shell under point load (S9)
  
• elastic large deflection of a curved beam (S10)
  
• finite rigid body rotation of a singly curved shell (S11)
  
• elastic large deflection response of a pear shaped cylinder under end shortening (S12)
  
• buckling and post-buckling response of axially compressed perfect and imperfect elliptical cylinders (S13)
  
• elastic large deflection response of a cylindrical shell with two diametrically opposite cutouts (S14)
  
• elastic large deflection response of a clamped square plate under uniform pressure (S15)
  
• post-buckling analysis of cylindrical shell under axial compression (S16)
  
• post-buckling behaviour of cylindrical panel under central point load (S17)
  
• expansion bellows under axial end load (S18)
  
• elastoplastic response of a spherical cap under a central load (S19)
  
• large deflection of a clamped cylindrical panel subjected to uniform pressure (S20)
  
• snap through of hinged cylindrical shell (S21)
  
• post-buckling of a simply supported circular plate loaded in radial edge compression (S22)
  
• elastic lateral buckling and large deflection response of a narrow cantilever beam (S23)
  
• elastoplastic lateral buckling of a narrow cantilever beam (S24)
  
• large deflection elastoplastic response of a circular plate (S25)
  

Available From

• R0009: 

  A Review Of Benchmark Problems For Geometric Non-Linear Behaviour Of 3D Beams And Shells

  
  
  

 

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A survey of possible benchmarks for 3D branched shells:

• elastoplastic behaviour of a stiffened cylindrical shell panel under compressive end load (BS1)
  
• post-buckling of stiffened panel under axial compression (BS2)
  
• elastic buckling of T-ring stiffened cylinders under external pressure (BS3)
  
• buckling of spherical shells ring supported at the edges (BS4)
  
• elastic buckling of I-ring stiffened cylinders under external pressure (BS5)
  
• 3D finite rigid body rotation of stiffened shell connected to a hinged bar (BS6)
  
• non-symmetric elastoplastic bifurcation buckling of a torispherical head with an axisymmetric nozzle (BS7)
  
• elastoplastic large deflection response of a multi-mitre pipe bend (BS8)
  

Available From

• R0009  

  A Review Of Benchmark Problems For Geometric Non-Linear Behaviour Of 3D Beams And Shells