The mechanical self-optimisation of trees

Due to the permanent competition in nature and the survival of the fittest, trees are highly optimised structures. The expenditure of energy and material for failsafe constructions would be uneconomically high for a species and a natural failure rate has to be accepted, but the optimisation prevents early failure. Five theorems are exemplified in the paper which describe the mechanical self-optimisation mechanisms of trees. - Minimisation of lever arms. Trees minimise stresses by reducing the length of the loaded lever arm. Length reduction can be achieved by active self-bending of stiff parts by forming reaction wood or through passive yielding of flexible parts of trees. - Axiom of uniform stress. Adaptive growth reduces stress-concentrations on the surface. Unavoidable stresses are distributed evenly on the surface of a tree. - Minimisation of critical shear stresses. Wood fibres are arranged along the force flow which minimises the shear stresses between the fibres. - Adaptation of the strength of wood to mechanical stresses. The wood quality is adapted to the degree and type of loading. - Growth stresses counteract critical loads. Residual stresses developed by the trees counteract axial compression and tangential tension caused by external loads and reduce the resulting stresses at the surface of the trees. Some of these biological optimisation mechanisms have been transferred by the Forschungszentrum Karlsruhe into engineering design processes and are used very successfully for the optimisation of technical components.