Description Qty Item Price  
your basket is empty

sub total£0.00  
£ $
proceed to checkout

Non-Linear Behaviour

material non-linear, general:

general set of benchmarks:

  • a review of numerous potential benchmark problems, not worked up into formal benchmarks

Benchmark P15 .

creep;

2D single element tests subject to secondary creep (Norton law):

  • plane stress with constant uniaxial load
  • plane stress with constant applied uniaxial displacement
  • plane stress with constant biaxial load (3 different ratios)
  • plane stress with constant applied biaxial displacement (3 different ratios)
  • plane strain with constant unequi-biaxial load
  • plane strain with constant applied unequi-biaxial displacement

3D single element tests subject to secondary creep (Norton law):

  • with constant unequi-triaxial load
  • with constant applied unequi-triaxial displacement

axisymmetric multi-element test subject to secondary creep (Norton law):

  • internally pressurised thick hollow cylinder

2D single element tests subject to primary creep (Norton-Bailey law):

  • plane stress with constant uniaxial load
  • plane stress with constant uniaxial stepped load
  • plane stress with constant applied uniaxial displacement
  • plane stress with constant biaxial load (2 different ratios)
  • plane stress with constant biaxial stepped load (2 different ratios)
  • plane stress with constant applied biaxial displacement (2 different ratios)

3D single element test subject to primary creep (Norton-Bailey law):

  • with constant unequi-triaxial load

2D single element tests subject to combined primary and secondary creep:

  • plane stress with constant uniaxial load
  • plane stress with constant uniaxial stepped load
  • plane stress with constant applied uniaxial displacement

Benchmarks R0027 , R0049 (subset of above), R0080 (subset of above).

3D multi-element test subject to secondary Norton creep:

  • torsional creep of long prismatic circular shaft under uniform twist held constant with time
  • torsional creep of long prismatic circular shaft under uniform twist steadily increasing with time

3D multi-element test subject to primary creep (Norton-Bailey law) with time hardening:

  • torsional creep of a square shaft under constant twist
  • torsional creep of a square shaft under steady twist rate

2D plane strain thick cylinder under temperature transient followed by fluctuating internal pressure:

  • both elastic-plastic and creep behaviour over 4 stages; non-proportional loading

Axisymmetric multi-element test subject to temperature-dependent secondary creep (Norton law):

  • thick hollow cylinder with temperature gradients and thermally dependent creep laws

Benchmarks R0026 , R0030 , R0049 (subset of above), R0080 (subset of above).

plasticity:

2D single element tests:

  • plane strain with perfect plasticity
  • plane strain with isotropic hardening
  • plane strain comparing kinematic and isotropic hardening
  • plane stress with perfect plasticity
  • plane stress with isotropic hardening

3D single element tests:

  • with perfect plasticity
  • with isotropic hardening

Axisymmetric test with perfect plasticity
Axisymmetric test with isotropic hardening
Plane strain cylinder incompressibility test

Benchmarks P06 , R0049 (subset of above), R0072 (subset of above), R0080 (subset of above).

2D two-bar assembly under constant axial load and cyclic temperatures of differing values in each bar:

  • with kinematic hardening and thermal load in one bar only, to test elastic shakedown
  • with kinematic hardening and larger thermal load amplitude, to test alternating plasticity
  • with kinematic hardening and thermal load in both bars, to test different elastic shakedown in each bar
  • with perfect plasticity and thermal load in one bar only, to test thermal ratcheting

2D beam with constant end load and cyclic temperature gradient:

  • with kinematic hardening, to test elastic/plastic shakedown and cyclic plastic strain accumulation

2D plane strain rigid punch test under prescribed displacements, with many elements:

  • with perfect plasticity, testing the solution towards the limit load
  • with isotropic bilinear hardening

Thin square plate with uniform load and perfect plasticity:

  • with simply supported edges, testing the solution towards the limit load
  • with clamped edges, testing the solution towards the limit load

2D plane strain thick cylinder under temperature transient followed by fluctuating internal pressure:

  • with both elastic-plastic and creep behaviour over 4 stages; non-proportional loading

2D plane stress half of an eccentric tube under constant internal pressure and cyclically varying through-thickness temperature gradient:

  • with perfect plasticity, testing ratcheting and alternating plasticity

Benchmarks R0026 , R0030 , R0049 (subset of above), R0072 (subset of above), R0080 (subset of above).

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)

Benchmarks P03 , R0065 (subset of above), R0072 (subset of above), R0080 (subset of above).

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)

Benchmarks P10 , R0010, R0065 (subset of above), R0072 (subset of above), R0080 (subset of above).

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)

Benchmarks R0024 , R0029 , R0065 (subset of above), R0080 (subset of above).

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)

Benchmark R0009 .

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)

Benchmark R0009 .

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)

Benchmark R0009 .

contact analysis:

2D multi-element plane strain tests:

  • contact patch test
  • rigid punch on deformable foundation
  • Hertzian contact
  • sliding wedge with linear springs
  • bending of a plate over a stiff cylinder
  • sliding and rolling of a ring on a rigid surface

2D multi-element plane stress tests:

  • cantilevered beam loaded against a rigid curvilinear surface

2D solid multi-element tests:

  • two contacting rings
  • buckling of a curved column with self-contact

2D axisymmetric multi-element tests:

  • interference between two cylinders

Benchmark R0081 .

Multi-element 2D/3D tests of a range of physical features:

  • 2D contact of cylindrical roller
  • 3D punch with rounded edges
  • 3D sheet metal forming
  • 3D loaded pin
  • 3D steel roller on rubber

Benchmark R0094 .