Fig. 1
Deformation function described by prismatic elements
Fig. 2
- Scheme of dam-rupture of Martin and Motce test (1958): (a) initial position; and (b) flow under open gate
Fig. 3
- FE meshes for dam-rupture model: (a) 38 cubic elements; (b) 324 cubic elements; (c) 392 cubic elements; and (d) 3004 linear elements.
Fig. 4
– Relative enlargement of the fluid base along time.
Fig. 5
– Detail of FE mesh for dam-rupture using 3004 linear elements: (a) Initial position, (b) Final position
Fig. 6
– Displacement fields of dam-rupture model using 392 cubic elements at different times: (a) , (b) , (c) .
Fig. 7
- Stress fields using 392 cubic elements (a) Static result – (b) Dynamic result at first time step ()
Fig. 8
- Pressure wave propagation of dam-rupture model using 392 cubic elements for the first 20 time steps.
Fig. 9
- Comparison of pressure profile of dam-rupture models: (a) Nithiarasu (2006)Nithiarasu, P. (2006). Erratun An Arbitrary Lagrangian Eulerian (ALE) formulation for free surface ows using the Characteristic Based Split (CBS) scheme (Int. J. Numer. Meth. Fluids 2005; 48:1415–1428), Int. J. Numer. Meth. Fluids, v. 50, p. 1119–1120.; and (b) proposed model
Fig. 10
- Scheme of solitary wave model of Laitone (1960)Laitone, E.V. (1960). The second approximation to cnoidal and solitary waves, Journal of fluid mechanics, v. 9, p. 430-444.
Fig. 11
- FE meshes of solitary wave model: (a) coarse (64 cubic elements), (b) fine (138 cubic elements); and linear (414 linear elements).
Fig. 12
- Vertical displacements given by our solution (coincident with Nithiarasu (2005)Nithiarasu, P. (2005). An arbitrary Lagrangian eulerian (ale) formulation for free surface flows using the characteristic-based split (cbs) scheme, Int. J. Numer. Meth. Fluids, v. 48, p. 1415–1428. )
Fig. 13
- Surface tension (St) influence - richer mesh
Fig. 14
- Comparison of displacement fields of solitary wave model using different meshes at three times: (a) t=2.4s; (b) t=7s; and (c) t=11.6s.
Fig. 15
– Bubble behavior along time (cubic approximation)
Fig. 16
– Position behavior of the analyzed bubble along time using a mesh of 4x4 cubic elements and bulk modulus
Fig. 17
– Pressure values () at time using a mesh of 8x8 cubic element and considering a damping of .
Fig. 18
– Analysis of the volumetric locking considering various bulk modulus and a mesh of 24x24 linear elements
Fig. 19
– Using a free node constrained movement to illustrate the volumetric locking in a 2D representation
Fig. 20
– Geometry and discretization used to model the oil passing through a funnel, (a) Dimensions and flow direction; and (b) Initial adopted mesh - Cubic - Structured 12x12
Fig. 21
– Pressure fields at various time () for the oil passing through a funnel model
Fig. 22
– Simplified slump test geometry and discretizations
Fig. 23
– Vertical displacement fields for different meshes and time, is the diameter of the base
Fig. 24
- Lower diameter behavior along time.
Fig. 25
– Creep tesr schematic representation and adopted discretization (linear elements).
Fig. 26
- Time response of stretch and viscous stress snapshots.
Fig. 27
- Viscous and elastic Cauchy stresses along time ().
Fig. 28
– Indirect relaxation test: (a) Material distribution; and (b) Discretization for a quarter of the problem (Symmetry)
Fig. 29
- Indirect relaxation test: (a) Initial position; and (b) Cauchy stress along time
Fig. 30
– Elastic case: Boundary conditions and transverse displacement
Fig. 31
– Sandwich viscoelastic plate: (a) Final displacement field, (b) Viscoelastic displacement at the plate center.
Fig. 32
– Central displacement along time for the sandwich plate viscoelastodynamic analysis
Fig. 31
– Sandwich viscoelastic plate: (a) Final displacement field, (b) Viscoelastic displacement at the plate center.
Fig. 32
– Central displacement along time for the sandwich plate viscoelastodynamic analysis