Analytical determination of the influence of geometric and material design parameters on the stress and strain fields in non-prismatic components of wind turbines

Abstract

Non-prismatic beamlike elements have long been used in engineering applications to optimize the performance of structures such as wind turbines, aircraft, and civil bridges, just to mention some examples. Unfortunately, engineering methods and formulas commonly used to analytically evaluate stresses and strains in prismatic beams do not hold and provide incorrect results for non-prismatic geometries. Large displacements and non-uniform material properties further complicate the analytical prediction. In order to determine the state of stress and strain in non-prismatic beamlike elements and its dependence on important design factors (such as taper parameters), a suitable mapping of the shape of such elements and a variational approach are used. The resulting field equations are exploited to derive application-oriented stress-strain formulas. Examples and comparisons with results of non-linear 3D-FEM analyses confirm the effectiveness of the modelling approach and of the new formulas proposed in this work.