Non-linear analysis

With Z88Aurora® V2 the possibility to  carry out non-linear simulations was introduced. Included are geometric non-linearities as a result of big displacements. This type of non-linearity occurs when drastic changes in the model geometry are caused by the structure’s deformation. Heavily deformed structures have a very high chance of displaying a stiffness behaviour with geometric non-linearities. This is why a non-linear solver should be used to calculate such structures to avoid huge  errors concerning the calculated displacements, forces and stresses.

The possibility to simulate material non-linearities was introduced in Z88Aurora® V3. They are a result of high stresses/strains and can be taken into account by providing the solver with addidtional material data, e.g. a stress over strain curve. This gives Z88Aurora® V3 the  capability to simulate plastic material behaviour, non-elastic deformations and spring-back effects. Furthermore the calculation of stresses is much more accurate for high loads. Also included is the possibility to calculate internal stresses, that result from a plastic deformation.

Z88Aurora® offers an iterative solver for non-linear calculations. Features include:

  • Supported element types for geometric non-linearities
    • Hexahedron No. 1 (linear) & No. 10 (quadratic)
    • Tetrahedron No. 16 (quadratic) & No. 17 (linear)
    • Plane stress element No. 7 and Torus No. 8
    • Truss 3D No. 4
  • Supported element types for plasticity
    • Hexahedron No. 1 (linear)
    • Tetrahedron No. 16 (quadratic)
  • Elastic-plastic material models:
    • von Mises
    • Wehmann & modified Wehmann
  • Spring-back analysis optional with varying number of steps
  • Results for each load step

Z88V14OS does not offer non-linear analysis options.

Thermal analysis

Many properties of components are temperature dependent and have to be investigated during their development.

With the help of steady state thermal finite element method designers and engineers are able to perform analysis of the thermal behavior of their product within each design phase. Due to a coupling of thermal and mechanical boundary conditions, it is possible to compute thermal results, such as temperature or heat flux, as well as thermal-mechanical displacements or stresses. This ensures that part temperatures during operation are within allowed limits. Possibly upcoming security issues can be examined and eliminated in an early phase of the product development process.

Z88Aurora® uses three numerical solvers for steady state thermal and thermal-mechanical simulations respectively:

  • Two different preconditioned iterative solvers with sparse storage for big finite element structures
  • One direct Multicore-solver (PARDISO) with sparse storage for medium-sized finite element structures
  • Available element types for thermal simulations:
    • Hexahedron No. 1 (linear) & No. 10 (quadratic)
    • Tetrahedron No. 16 (quadratic) & No. 17 (linear)

Unfortunately it is not possible to perform thermal analyses by Z88V14OS.

Natural Frequency Analysis

Intended or not intended resonance phenomena are well known to everyone out of daily life, even if it’s not obvious to us that natural frequencies play a roll – for example a mother pushing her child on a swing exactly at the peak, giving more energy to the resonance system “swing-child” this way.

With a technical system the transmission of more energy leads during resonance – i. e. the externally forced excitation frequency equals one of the eigen frequencies – leads to an overly high amplitude and therefore to an unavoidable destruction of the system, the so-called resonance catastrophe. Especially in civil engineering this is the worst case scenario and is to be avoided under every circumstance. Therefore, one has to determine every eigen frequency of the system, at which accelerating and restraining forces, induced by mass inertia or restoring forces from stiffness properties, balance each other. This can be done via finite element based natural frequency calculation (modal analysis). These frequencies are characteristic for every object and have a corresponding shape which would assume the shape of the displacements of the object when rocking with this specific natural frequency. With the help of the physical property obtained by simulation, the designer can draw his conclusions to unmatch practical relevant loadcases with the structure’s natural frequencies.

In Z88Aurora® you can use a Lanczos solver for natural frequency calculation. Features include:

  • Supported elements:
    • Hexahedron No. 1 (linear) & No. 10 (quadratic)
    • Tetrahedron No. 16 (quadratic) & No. 17 (linear)
  • Lanczos solver to calculate eigenvalues and modal form vectors
  • Incremental display of natural frequencies via the postprocessor
  • Individually selectable number of calculated eigenmodes

Unfortunately, Z88V14OS does not offer modal analyses.