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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)

**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

## 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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**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

## 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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**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

## 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 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)

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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)

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