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# 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)

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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)

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**R0010**

## 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)

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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)

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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 elasto-plastic 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)

- elasto-plastic 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)

- elasto-plastic 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)

- elasto-plastic lateral buckling of a narrow cantilever beam (S24)

- large deflection elasto-plastic response of a circular plate (S25)

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## A survey of possible benchmarks for 3D branched shells:

- elasto-plastic 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 elasto-plastic bifurcation buckling of torispherical head with axisymmetric nozzle (BS7)

- elasto-plastic large deflection response of a multi-mitre pipe bend (BS8)

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