The paper presents a theoretical framework of a more comprehensive methodology of analysis of behavior of homogeneous and composite materials and structures. The behavior of bolted flanged connections is taken as an illustrative example. Particular attention is given to the local effects. The term “local effects” denotes the actual, pronounced local three-dimensional stress states which exist in particular regions of the actual, weakly three-dimensional, stress fields occurring in plates and shells. Presented examples show that the local effects can be one of the major causes of failures of homogeneous or composite laminated structures. Within the chosen theoretical framework, an outline of new analytical/experimental methods is presented, called isodyne methods. It is demonstrated that the isodyne methods allow the determination of the normal and shear components of the stress states in plates and beams, including the three-dimensional stress states at the crack tips, tips of local disbounds or defects, or in the lamination planes.