Optimization model preparation
Controlling tension/compression

In many practical applications it might be useful to have some influence on the ratio of tensile and compressive stress magnitudes. Some of possible situations are as follows:

• The used material exhibits different values of yield strength in compression and tension. Adequate stress levels can substantially improve structural efficiency.
  
  
• The structure under consideration undergoes cyclic loading so that some parts are always in tension and the other always in compression. A reduction of tensile stresses may help preventing crack initiation and propagation (fatigue cracks).
  
  
• The material used exhibits creep behavior and the creep effects differ in tensile and compressive regions. In such situations adequate stress levels can also be of much benefit.

ProTOp offers a material parameter, here termed the tension to compression strength ratio, that can be engaged to favor compression regions on the account of tension regions, or vice versa. This parameter is defined as:

TenComRatio = (Material tension strength) / (Material compression strength)

The default value of this parameter is TenComRatio = 1.0, but this value can be changed as desired for each individual material separately.

An illustrative example

The figure below shows an example of a cantilever structure optimized with TenComRatio = 1.0. The colors displayed indicate averaged Mises (AM) stresses and one can see that the lower and upper parts of the structure are equally stressed and of the same thickness.

Figure. Symmetrically distributed Mises stresses in the optimized 2D cantilever.

At the tip, the structure is loaded in the downward direction which results in the upper structural parts to be in tension while the lower structural parts are in compression. In ProTOp this can be easily visualized by displaying the signed averaged Mises (SgnAM) stress. The regions in tension are displayed in red colors and the compressed one in blue colors.

Figure. The signed averaged Mises (SgnAM) stress reveals tension and compression regions.

By setting TenComRatio = 0.75 and running a few optimization cycles, material is redistributed so that the tensioned regions are stressed less on the account on higher stresses in the compressed regions. In the figure below one can clearly see that in the new design the tensile regions are reinforced on the account of compressed regions. In case of time varying load amplitude, this could significantly lower the probability for eventual crack initiation.

Figure. Tension regions are reinforced on the account of compression regions.

By further reduction to TenComRatio = 0.5 and running a few additional optimization cycles, material is redistributed even more. In the figure below one can clearly see that in the new design the tensile regions are further reinforced on the account of reduced or vanishing compressed regions.

Figure. Tension regions are reinforced on the account of reduced or vanished compression regions.

By setting the TenComRatio parameter smaller or larger then 1.0, the actual stress levels within the structure are adjusted in accordance with this parameter. Either the stresses in tension regions are reduced on the account of those in the compression regions or vice versa.

Figure. Averaged Mises stress levels in the structure are adjusted in accordance with the tension to compression ratio.