∞3 Hierarchy plate theories for thick and thin composite plates: The generalized unified formulation

Generalized Unified Formulation shell element for functionally graded Variable-Stiffness Composite Laminates and aeroelastic applications

“…Another option, on which the present effort is based upon, is represented by the so-called Compact Notations (CNs) (see Ref. [26] for more details). The idea behind CNs is to write the axiomatic expansions in indicial form, so that all the possible theories can be generated from theory-invariant kernels (also referred as nuclei).…”

“…With the present effort, the authors introduce the Generalized Unified Formulation (GUF) [26,32,[27][28][29][30][31]33] for VAT structures for the first time.…”

A state space augmented generalised RKPM for three-dimensional analysis of thick and laminated composite plates

“…Using Reissner's mixed variational theorem in conjunction with the principle of virtual displacements, Carrera [15] introduced a compact and unified formulation for LLT which successfully satisfies the requirements for the continuity of interlaminar stresses and piecewise continuous displacement field. Demasi [16][17][18][19][20] further developed ''Carrera's Unified Formulation'' (CUF) and presented ''Generalized Unified formulation'' where in both formulations a variety of refined and mixed laminated plate theories can be obtained by choosing the desired orders used for expansion of field variables. It is noteworthy that although the accuracy of the LLT is significantly greater than the ESLT, they are generally computationally expensive because the number of unknowns in the problem is also dependent on the number of laminates.…”

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part I: Model formulation

“…First, generalised higher-order theories are preferred over Levinson-Reddytype models as the latter lead to static inconsistencies at clamped edges [16]. Second, an arbitrary-order theory can be conveniently expressed using the unified formulations of Carrera [9,17,18] and Demasi [19] by expressing the displacement field as a generalised axiomatic expansion in terms of a Taylor series or Lagrange polynomials. Third, a fundamental characteristic of purely displacement-based theories is that all strains and stresses are derived from the displacement assumptions using the kinematic and constitutive equations, respectively.…”