Solvers and performance
- New iterative solver with parallel processing
- Optimized solver performance in nonlinear analysis
- Line to solid interfaces for 3D bond-slip analysis
- 3D membrane elements for modelling geogrids
- Eccentricity in curved shell elements
- Distributed mass elements for dynamic analysis
- Total strain crack models in combination with Kelvin viscoelasticity
- Definition of Kelvin and Maxwell chains from creep-relaxation curves
- Definition of orthotropic thermal and concentration expansion in combination with nonlinear analysis
- Definition of axial force-elongation and moment-curvature diagrams in class I beams
- Jointed rock plasticity model foe modelling stratified or jointed rock
- Duncan Chang soil model
- Simplified Coulomb friction model
- Definition of pressure head dependent conductivity and storativity
- Staggered analysis also with linear structural elements
- Results at the element center point
- Concrete biaxial failure envelope
- Summed crack strains
- CQC combination in Spectral Response Analysis
- User supplied subroutine for design checks in beams, shells and plates
- Dynamic pressures in fluid-structure analysis
- Shear and hydrostatic stress capacity against Mohr-Coulomb failure
Pre- and post-processing
Update to CADfix library 7.1 SP3
Creation of reinforcement bars from geometry lines FEMGEN
Creation of reinforcement grids from geometry surfaces FEMGEN
Labeling DIANA element types in FEMVIEW
Labeling and coloring reinforcements in FEMVIEW
FX+ for DIANA
Definition of properties in interface elements
Input of distributed moments
Definition of reinforcement groups
Definition of frequency load factors
...and more (see DIANA 9.4 Release Notes)
New iterative solver with parallel processing
The parallel direct solver that was introduced in DIANA 9.3, PARDISO, is especially efficient for models made of shell elements. However, the efficiency of PARDISO is invalidated by the excessive memory use made by direct solvers in case of large 3D models with solid elements. In this case the stiffness matrix is usually good conditioned and smaller memory use can be achieved with iterative solvers. DOMDEC, Domain Decomposition Solver, is the new iterative parallel solver available in DIANA 9.4. Speed-up of parallel analysis can be achieved at condition that the memory bus of the machine is sufficient. DOMDEC has been tested and shows excellent performance on Intel® Core™ i7 processors, which are the state of the art in multi-core technology.
Application examples of DOMDEC
Non-linear analysis of a beam
The model is shown in Figure 1. a beam, supported at the ends, is subjected to the own weight, and to a pressure load applied on a steel plate at the middle of the beam. The pressure load is applied in 305 loading steps.
The beam consists of 12600 brick second order brick elements (CHX60) and 56 reinforcement bars, which model longitudinal reinforcement and stirrups, for a total of 185250 dofs. A total strain crack model is assumed for concrete, and von Mises plasticity model is assumed for steel. This analysis was performed on a HP Proliant BL460c server.
This is a typical example of application of an iterative solver. The band width of the stiffness matrix is relatively high, because high order brick elements are used. As a consequence, the use of memory is also high.
The graph in Figure 2 shows the performance of DOMDEC for this analysis, for one of the loading steps. The two curves refer to the total solution time (which also includes time necessary to store/retrieve data from the DIANA database) and to the effective solver time. For the run with one processor only, the total solution time of the standard DIANA iterative solver is compared with the total solution time of DOMDEC.
The total solution time reduces from 171 sec in case of standard DIANA iterative solver up to 38 sec in case the new iterative solver is used on 8 processors, with a gain of about 2 minutes time.
Linear analysis of a gas field
The model consists of 800.000 linearly interpolated tetrahedral elements (TE12L) and 40.000 plane triangular interfaces (T18IF), which describe the slipping faults. The total number of nodes in the model is 156000, for a total of 468000 dofs.
The performance of DOMDEC for this analysis is shown in the graph of Figure 3.
Optimized solver performance in nonlinear analysis
Choice of the solution procedure is automatized in DIANA 9.4. At each step, the factorized matrix from the previous converged step is used for preconditioning. In case minor changes have occurred in the stiffness matrix between the two steps, this brings to the exact solution of the system of equations. Vice versa, the whole solution procedure will take place.
The advantage of this new functionality can be appreciated especially in dynamic non linear analysis, where changes in the stiffness matrix between two steps are only local.
Line to solid interfaces for 3D bond slip analysis
Typical applications of this type of elements are:
- analysis of pile raft foundations, where the piles are modelled with beam elements embedded in the surrounding soil;
- analysis of bond slip in reinforcement bars, where the reinforcement bars are modelled with truss elements embedded in the surrounding concrete;
- analysis of anchors and anchor losses.
In both cases the beams/trusses are initially modelled as reinforcements embedded in solids. Simply by defining INTERF in the DATA table (see Figure 4), the reinforcement particles are automatically converted to beam/truss elements, and the interfaces are automatically generated.
Material constitutive models that can be assigned to these interfaces are:
- multi-linear relationship between traction and relative displacements at the nodes of the interfaces;
- bond slip constitutive models.
Different slip properties can be defined as space function.
Figure 5 shows an example of analysis of a raft pile foundation. Figure 5a shows the whole model of the raft foundation, the piles and the stratified soil. Figure 5b shows only the raft foundation and the piles.
Figure 5a & b
This example could be enriched by including possible tip failure of the piles by introducing a non linear spring at the end of the pile.
3D membrane elements
This new family of elements consists of 3D flat or curved surfaces with only in plane stresses. These elements are mostly suitable for modelling canvas and geogrid structures.
Distributed mass elements
These elements can be used in dynamic analysis for taking into account the interaction between fluid and structure, using the approach of added masses instead of the fluid-structure interaction module available in DIANA. Distributed mass elements can be line or surface elements, with the possibility of defining the effect of the added mass both in the direction normal and tangential to the element. The common Westergaard distribution of added masses can be adopted in DIANA.
Eccentricity in curved shell elements
Curved shell elements may be connected eccentrically to the nodes (see Figure 7). Eccentricity can vary in the same element for each node. The corresponding generalized forces and moments are calculated with reference to the surface containing the nodes of the shell.
Total strain crack models in combination with Kelvin viscoelasticity
Among DIANA users total strain crack models are more popular than smeared crack models based on crack strain formulation. One of the disadvantages of this type of crack models was until now the impossibility of combining them with creep. After request from the nuclear power industries, this functionality has been made available in DIANA 9.4. For taking into account creep behaviour, the total strain used in the crack model formulation is simply cleansed from the creep component of strain.
Orthotropic thermal and concentration expansion in combination with nonlinear analysis
Orthotropic thermal expansion and orthotropic concentration expansion can now also be applied in nonlinear analyses. Thermal and concentration expansion strain components can be output in both local and global directions.
Definition of Kelvin and Maxwell chains from creep-relaxation curves
When creep or relaxation curves are specified, DIANA determines automatically the parameters of Maxwell or Kelvin chains. In DIANA 9.4 these parameters are written to the .OUT file.
Definition of axial force-elongation and moment-curvature diagrams in class I beams
Definition of generalized stresses and displacements in beams is common engineering practice. This is now also possible in DIANA 9.4, where multi linear axial force-elongation or moment -rotation can be defined both for 2D and 3D class I beams.
Jointed rock plasticity model
The Jointed rock model is an anisotropic elasto-plastic model for modelling stratified or jointed rock formations. In this model different stiffnesses are adopted in the direction normal to the stratification and in the two in plane directions. A non associated non hardening Coulomb model can be defined for each shear failure plane.
Figure 8 gives an example of definition of material properties in the Jointed rock model. This material model can be applied in combination with plane stress, plane strain, axis-symmetric, and solid elements, and with modules *LINSTA and *NONLIN
Figure 9 shows the shear stress contour plot in a jointer rock medium with layers inclined of 30º to the horizon, when a tunnel is excavated.
Duncan Chang soil model
The Duncan Chang model is a classic nonlinear soil model, widely accepted in engineering practice. In this model, the shear stress is defined as an hyperbolic function of the axial strain derived from a triaxial test. This model can be combined with plane stress, plane strain, axis-symmetric, solid elements and module *NONLIN.
Simplified Coulomb friction model
The Coulomb friction model has the disadvantage to require a large memory use as consequence of the non symmetric stiffness matrix. The problem of a non symmetric stiffness matrix is overcome in the new Non linear friction model, that is a non linear elastic model available in DIANA 9.4.
Definition of pressure head dependent conductivity and storativity
Pressure head dependency of conductivity and storativity can be defined in DIANA 9.4 using predefined functions next to multi-linear diagrams. The Gardner and Frontal Function are available for defining conductivity. The Van Genuchten function is available for defining storativity.
Staggered analysis also with linear structural elements
In order to guarantee compatibility of the strain field in the flow domain and in the structural domain, flow elements an order lower than the structural elements should be used. This may result in models with a very large number of dofs and poor performance. For this reason the possibility of performing staggered analysis also in case linearly interpolated structural elements are used has been added in DIANA 9.4.
Results at the element center point
One of the issues arising in non linear analysis is the giant size of the output files. In case of large models or large number of steps, the user might end in being unable to manage the output files, especially if many result components are required in output. For this reason the functionality of output the results at the center point of each element has been added in DIANA 9.4. In this manner, not only the output files are reduced in size, but the results are also presented in a form that is more suitable for structural design purposes. In fact, the user can easily identify those elements that fulfil or fail a given design criterion.
Concrete biaxial failure envelope
The concrete failure safety factor according to ACI 209 can be calculated and output for linear elastic models. For applying this output functionality the user needs to define additional parameters in the MATERI table, such as the concrete compressive strength and its eventual ambient dependency, as well as safety factors for Static and Dynamic conditions, Usual, Unusual and Extreme conditions. Figure 10 shows a typical failure envelope and the contour plot of safety coefficients in an arch dam: in red are the where the safety coefficient is lower than 1.
Summed crack strains
When the multi-directional crack model and the total strain crack model are applied, several cracks can occur at the same integration point. In the previous releases of DIANA, the crack strain at a given integration point was calculated for each crack. In this manner, processing results was a lengthy and tedious operation. In DIANA 9.4 it is possible to output the summed crack strains at each integration point. For each crack, the crack strain is decomposed along the directions of the element reference system. Then, for each direction, the corresponding crack strain components are summed. In this manner, the crack strain can be output as vector (if referred to the local reference system) or tensor (if referred to the global reference system). Furthermore also the principal crack strains can be output.
Figure 11 shows the principal summed crack strains in a beam that fails in shear.
CQC combination in Spectral Response Analysis
The spectral response analysis procedure has been extended in DIANA 9.4 with the Complete Quadratic Combination (CQC) mode superposition method. In this superposition method the correlation among the modes is addressed explicitly by introducing correlation coefficients, which vary between zero and unity. These correlation coefficients are calculated from the modal damping ratios.
User supplied subroutine for design checks in beams, shells and plates
For linear elastic analysis DIANA the user can use a user supplied subroutine for defining results derived from forces and bending moments acting on the cross sections of beams, shell and plates. In this manner the user can specify specific code checks, and include these code checks in the DIANA tabular output. For scalar derived results the output is also available in iDIANA and FX+.
Dynamic pressures in fluid-structure analysis
The dynamic pressures of fluid-structure interface elements can be output in modal response analysis, direct response analysis, and nonlinear transient analysis. The dynamic pressure of the fluid on the structure is calculated as product of the acceleration normal to the interface and the effective mass of the water.
Figure 12 shows the results of an earthquake analysis of an arch dam. Figure 12a shows the deformed shape of the dam at a given step. For the same step, Figure 12b shows the cracks forming in the dam and Figure 12c shows the distribution of dynamic fluid pressure.
Shear and hydrostatic stress capacity against Mohr-Coulomb failure
The shear capacity ψ and hydrostatic pressure capacity χ against Mohr-Coulomb failure can now be output for linear elastic models. this allows the user to check the model against stability. ψ and χ are calculated according to the formulae:
Ψ = q /qmc and χ = (3-sin ϕ)/(6sin ϕ)*(qmc-q)
where the material parameters ϕ and qmc are defined by the user. This output functionality is available in modules *LINSTA, *NONLIN and *SPECTR.
Update to CAD-fix library 7.2 SP3
In FEMGEN the CADfix libraries are updated to the latest version. In this manner a wide range of the most recent CAD formats can be handled in iDIANA.
Creation of reinforcement bars from geometry lines FEMGEN
This functionality allows the definition of reinforcement sections directly from lines or surfaces, instead of coordinates. In this manner, reinforcement can be defined in a straightforward manner also in models that are imported from CAD.
Labeling and coloring reinforcements in FEMVIEW
New commands have been added in iDIANA/FEMVIEW for visualizing element types and reinforcement particles:
- LABEL MESH VARIANTS enables to label all elements with the element type name. Reinforcement particles are labeled with their keyword BAR or GRID followed by their reinforcement number.
- VIEW OPTIONS COLOUR VARIANTS enables to color all regular elements green and reinforcement particles orange.
- CONSTRUCT SET APPEND VARIANTS enables to append elements of the specified variant (element type or reinforcement) to a set
- CONSTRUCT SET REMOVE VARIANTS enables to remove elements of the specified variant, (element type or reinforcement) from a set.
Definition of interface elements properties in FX+
In FX+ for DIANA it is now possible to define the material properties for interface elements through a dedicated dialogue that includes all interface material models available in DIANA. See Figure 13.
Input of distributed moments in FX+
In FX+ it is now possible to define distributed moment acting on edges or faces of plates and shells.
Definition of reinforcement groups in FX+
In FX+ it is now possible to create groups of reinforcements. In this manner, management of reinforcements both in input as in output is easy for the user. In fact, not only it is possible to visualize different reinforcement by choosing the corresponding reinforcement sets, but it is also possible to select specific reinforcement groups for visualization of the results.
Definition of frequency load factors in FX+
The frequency load factors, that are specified in DIANA in the table FREQLO, can now also be specified in FX+. See figure 14.