A minimisation algorithm with application to optimal design of reinforcements in textiles and garments

Purpose This paper aims to develop an efficient two‐variable minimisation algorithm and to apply it in engineering optimisation of buttonhole reinforcements. Design/methodology/approach An iterative extreme search is based on quadratic approximation of objective function, locating approximate solution at the minimum of corresponding elliptic paraboloid. Stress analysis is performed using plane stress finite element model. Optimal selection of geometrical parameters of buttonhole‐type reinforcement is done in terms of balance between maximum stress and material consumption. Findings Adopted minimisation algorithm is assessed in a selected test example and proven to perform well in comparison with methods available in literature. In the selected case two local minima have been found within the predefined optimisation domain, with slight difference in objective function values. Research limitations/implications Research is limited to homogeneous isotropic elastic model and a single representative load case. Objective function is restricted to two influence factors and predefined optimisation domain. Practical implications The method can be useful for engineers/practitioners in the branch of clothing technology as a tool for computational estimate of optimal design of structural reinforcements. Originality/value The main quality of the paper is in software fusion of finite element analysis and advanced optimisation algorithm. The proposed theoretical‐numerical model is discussed in terms of applicability in parameter setting on buttonholer in garment production.