Interaction mechanics of localized shear loads in infinite FRC strips: A displacement-function approach

An alternative analytical framework is proposed for investigating the mechanics of interacting shear loads in infinite fiber-reinforced composite strips. The composite-strip problem is formulated in terms of a displacement-function of spatial variables, defined through the displacement components of plane elasticity and governed by a single partial-differential equation of equilibrium. Single and paired localized shear loads are applied over the central region of the strip, while mixed boundary conditions are imposed at the distant lateral boundaries of the quasi-infinite domain. A comprehensive parametric investigation is performed to examine the effects of loading region, load spacing, loading direction, and fiber orientation on the induced stress and deformation fields. The results reveal that the axial stress component governs the overall stress state, whereas severe local stress concentrations develop near the leading and trailing edges of the discrete shear loads. The convergence characteristics of the series solution is evaluated at both singular and regular locations with respect to the number of terms in the series and loading extent. Finally, the displacement-function solutions are validated against classical elasticity solutions and finite-element simulations, showing excellent agreement except near localized singularities. The proposed framework provides an efficient and reliable alternative for analyzing interacting shear loads in composite strip structures.