Extension of Boley’s continuum mechanics-based successive approximation method to two-layer rectangular beams

Abstract An extension of Boley’s continuum mechanics-based successive approximation method is presented for rectangular beams composed two isotropic linear elastic layers. The solution cast into the form tables, in complete analogy to tables originally by Boley and Tolins single-layer strips. first column these corresponds classical Bernoulli–Euler theory beams. further columns represent comparatively fast converging correction terms an increasing refinement. Our two-layer formulation automatically satisfies stress continuity conditions at interface Enforcing displacement between layers, we derive results that do satisfy equilibrium field equations, boundary upper lower edges. When converged, constitutive relations layers are also satisfied. We present a compact formulation, which allows writing down more than three steps considered Tolins. elasticity solutions subsequently can be used as novel analytic benchmarks comparison with refined structural mechanics beam theories. Interior finite axial extent obtained assigning approximate lateral ends. Comparisons element computations clamped–clamped give strong evidence correctness our results.