Accuracy of cross-section stress numerical integration by boundary integration formulae

Computing of internal forces of the bar cross-section for given deformation is a necessary step in most computations related to the bar structures. Internal forces are integrals of stress in a section area. Integrating stress for arbitrary cross-section shape is tedious and the use of boundary integral approach combined with numerical integration can simplified computations. Misunderstandings about possible numerical integration of section stress accuracy and efficiency can be found in literature. Numerical integration errors depend on adopted integration scheme. First, the results for 1D test case for some number of integration schemes are demonstrated. Having this in mind examples from literature are reanalysed.