Multilayered and sandwich structures are extensively utilized in aerospace, automotive, and marine applications due to their superior stiffness-to-weight ratios. However, their accurate modelling remains computationally challenging. Classical theories such as FSDT and ESL lack the capability to capture layer wise effects, while discrete-layer and 3D finite element models are often computationally prohibitive. This paper introduces ZZA_GEN, a generalized physically based zig-zag theory that overcomes these challenges by allowing user defined through-thickness displacement representations and abandoning rigid coefficient roles. Derived from the Zig-Zag Adaptive (ZZA) theory, ZZA_GEN achieves high fidelity in stress and displacement prediction with minimal computational overhead. It retains the simplicity of a C0 finite element formulation while maintaining accuracy equivalent to higher-order theories. Validation against classical benchmarks, including elastostatic and dynamic problems, shows excellent agreement with 3D FEA results. The theory's adaptability and integration potential with commercial solvers make it highly suitable for industrial applications.