# Linear analysis In the 50s, the linear finite element method was the starting point for the success story of FEM calculations in praxis.

With this type of calculation, it is assumed that the results are proportional to the loads. Through this assumption the solution of the problem becomes much easier.

Nevertheless, this method has not served out yet. Most of daily life objects deform linear elastic in certain ranges. Therefore the linear FEM is the easiest and fastest method to conduct calculations. It gives important information on component strength and possible weaknesses to the designer.

Z88Aurora

Z88Aurora® offers four numeric solvers for systems of equations for linear static calculations:

• A direct Cholesky solver with Jennings storage method for small beam and bar structures
• Two differently preconditioned iterative solvers with sparse storage for large finite element structures
• One direct multicore solver (PARDISO) with sparse storage for mid-sized finite element structures

These solvers have the following features:

• 25 integrated finite elements:
• Structural elements (bars, beams and shafts)
• Continuum elements (tetrahedrons and hexahedrons) with different shape functions
• Various special elements (e. g. shells, continuum shells, tori and plates) with different shape functions (linear, cubic)
• The calculation of stresses can be done via three different stress hypotheses:
• von Mises
• Rankine
• Tresca

Z88OS

With Z88V15OS the following solvers are available for linear static calculations:

• A direct Cholesky solver with Jennings storage method
• A spare matrix iterative solver (CG preconditioned) for very large structures

The Z88OS solvers have the following features:

• 25 integrated finite elements:
• Structural elements (bars, beams and shafts)
• Continuum elements (tetrahedrons and hexahedrons)
• Various special elements (e. g. shells, continuum shells, tori and plates)
• Various shape functions from linear to cubic
• Calculation of stresses via three different stress hypotheses:
• von Mises
• Rankine
• Tresca