A general computational approach for the axial load-carrying capacity of the multi-beam structure

The methodology to compute the lowest axial load-carrying capacity for a multi-beam structure has been presented in several articles either using numerical methods or an analytical approach. It has been proved that the beam length inequality significantly affects the load-carrying capacity, and the beam load–displacement relation must be included into calculation. The previously derived approach to compute the lowest carrying capacity, where the beam load–displacement relation is expressed by a piecewise function, is enhanced in this paper by using a single-expression function, which makes the calculation much simpler. As a single-expression function, the power-exponential function, rational function, and a sum of Weibull functions are presented, where the undetermined coefficients are calculated to fit the load–displacement curve obtained by the finite element method. Since the beam finite elements are not always suitable in practical applications, an approximation procedure for solid elements is presented that provides the load–displacement relation for further computation. The conventional approach to calculate the axial load-carrying capacity of a multi-beam structure by the finite element method is reduced to express the load–displacement relation for a single beam by a single-expression function and perform the optimization process. The developed approach provides faster and simpler computation of the lowest axial load-carrying capacity, where the correctness is proved by the experimental analyses and complex finite element analysis.