Stresses, Failure Criteria & Resolution Levels

For each scenario and iteration, a Failure Criterion is calculated which represents the goal of the optimisation and based on which the design is generated.

A Failure Criterion value of 1 is always the objective of the optimisation. Four different types of Failure Criteria are available (von Mises Stress, FFF Thumb Rule, Directional Dependent Tsai-Hill or Tsai-Wu). More information regarding the Failure Criteria here.

The Safety Factor calculates the goal for the optimisation in regard to the material properties (material limits) for the chosen Failure Criterion. The following two examples show how the goal for the optimisation is calculated:

For an isotropic material, the von Mises Stress is chosen as the Failure Criterion. The Tension Strength of the material is 200 MPa. The Safety Factor is set to 4, this means that the goal of the optimisation is to load all the material with a stress value of 50 MPa (Stress Goal).

Material Properties	Value	Safety Factor	Stress Goal

Material Properties	Value	Safety Factor	Stress Goal
Tension Strength	200 MPa	4	50 MPa

For an 3D Orthotropic material the directional dependent Tsai-Hill is chosen as the Failure criterion. The Tension Strength in build direction is 200 MPa, the Tension Strength in in-plane directions is 240 MPa and the Shear Strength is 120 MPa. The Safety Factor is set to 4, this means that the material can be loaded in build direction with 50 MPa, in in-plane directions with 60 MPa and the Shear Stress with 30 MPa.

Material Properties	Value	Safety Factor	Stress Goal

Material Properties	Value	Safety Factor	Stress Goal
Axial Tension Strength (build direction)	200 MPa	4	50 MPa
In-Plane Tension Strength	240 MPa	4	60 MPa
Shear Strength	120 MPa	4	30 MPa

The calculated Stress Goal / Failure Criteria values are the overall goal for the optimisation and have a big influence on the resulting design. The goal is that the material of the part is evenly loaded and the stress uniformly distributed. Thus, the Stress Goal isn’t the maximum stress which can occur at Design Space limits or due to FE singularities, but the value which is a good middle value for a long part life (green areas in the example above). Only in exceptional cases the yield strength of the material is the best value for this parameter which corresponds with a Safety Factor of 1, e.g. when the applied loads are too small to result in such stresses.

By changing the Stress Goal/Safety Factor, the stiffness of the structure can be influenced as well. Due to uniformly distributed stresses, lower Stress Goals result in stiffer parts at the most lightweight design.

Stresses & Failure Criteria in Combination with the Resolution

The used Stress Goal / Failure Criterion is dependent on the resolution level during the optimisation. The optimisation runs on different resolution levels and switches between them to achieve the best results. The first iterations are calculated on a coarse resolution level. With rising number of iterations, the resolution gets finer. This means that the first iterations calculate much faster than the last iterations but aren’t as detailed as the last. With the increasing resolution, the size of the output data, the calculation time as well as the surface quality increase.

For each resolution level a different Safety Coefficient is defined. The Safety Coefficient is a value between 0-1 and is multiplied with the chosen Stress Goal / Failure Criterion. On the lower resolution levels the value is beneath 1 and on the highest resolution level exactly 1. Thus, on the lower resolution the optimisation target is scaled to a lower value. On the highest resolution level, the requested Stress Goal / Failure Criterion reaches 100% and thus satisfies the defined Stress Goal / Failure Criterion as the geometry allows it.

In one optimisation several Events (load cases) can be considered. Each Event is calculated by itself and the stresses / Failure Criteria of all Events are enveloped and the highest value for each area is considered. For information regarding the Event Specific Safety Factor have a look here.

The Stress / Failure Criterion calculation is from an FE point of view an estimation. That’s why we recommend a FE-Reanalysis using Apex Structures/Nastran to verify the results regarding all boundary conditions. For the reanalysis the Nominal-Geometry should be chosen which will be used after manufacturing and post manufacturing processes. The Reanalysis can also take dynamic loading & other boundary conditions into consideration that are not considered in the design process.

For further information regarding the stresses and Failure Criteria in the Post Processing, have a look here.