Accurate mechanical and multiphysical analysis of layered structures using high-fidelity models are required to generate benchmark solutions. This process is necessary to identify the inaccuracies in solutions from approximate mathematical models and com-
putational methodologies employed for specific applications. The state space method (SSM) and the state space-differential quadrature method (SSDQM) have been successfully used to develop the exact formulation and obtain accurate analytical and semi-
analytical benchmark solutions for multi-layered plate and panel structures. The present work identifies some of the limitations of these methods for analysis of multi-layered plates and proposes simple and general procedures to improve them and extend their applications.

A novel procedure is proposed to extend the application of SSM to functionally graded plates with multiple layers of exponential and/or non-exponential gradation. Additional matrices are introduced to enforce the correct continuity conditions at material interfaces. These additional matrices within piecewise exponential functions enable
analysis of non-exponential gradation in the layers. The extended SSM is verified and used for three dimensional elastic and thermoelastic deformation analysis. A detailed parametric study is performed to show that the extended SSM provides accurate analytical solutions for graded plates and sandwich panels. For two-dimensional analysis of plates using SSDQM, a systematic and general approach is proposed for implementing arbitrary edge boundary conditions. The proposed modified SSDQM is verified for various combinations of edge boundary conditions and later used to study the free vibration response of thick, soft-core sandwich panels.

The proposed approach is shown to provide faster convergence compared to the conventional SSDQM that uses ad hoc procedure for implementing edge boundary conditions. A simple and general approach, compatible with the one developed for elasticity analysis, is proposed for two-dimensional piezoelasticity analysis using SSDQM to implement edge boundary conditions in a systematic manner. The method is verified for various mechanical and electrical edge boundary conditions and applied to model the bending and free vibration response of thick, piezoelectric laminates.

A simplified mathematical condition is derived from the inherent mathematical constraints of SSDQM to develop a general and flexible approach for two-dimensional elasticity analysis of layered panels with mixed boundary condition through the thickness of the same edge. Bending and free vibration response of thick, soft-core sandwich panels with different edge conditions on face sheets and core are studied.

The systematic procedures introduced in the present work successfully removed limitations in the current implementation of the SSM and SSDQM. The extended SSM and modified SSDQM enable accurate analysis of the mechanical and multiphysical response of layered plates with large thickness-to-length ratio, high inter-layer stiffness ratio, non-exponential material gradation, multiple fields and mixed edge bound-
ary conditions. The generality and simplicity of the proposed procedures will enable their extension to curved beams/plates, circular/annular plates, cylindrical shells, etc.