Axiomatic/asymptotic analysis of refined layer-wise theories for composite and sandwich plates

Abstract

This paper deals with layer-wise (LW) models for composite and sandwich plates. Refined layer-wise models are built according to the Carrera Unified Formulation (CUF) which has been developed over the last decade for beams, plate and shell theories. CUF allows the hierarchical implementation of refined models based on any-order expressions of the unknown variables. In this paper, displacement variables are expanded along the layer thickness through Legendre polynomials. Comparisons with previous analysis based on Equivalent Single Layer (ESL) approaches are given. The effect of each term of the expansion on the accuracy of stress/displacement components for the static response of composite and sandwich plates is analyzed. Ineffective terms are discarded from the expansion in order to save computational cost. The reduced models obtained, which are denoted as mixed axiomatic/asymptotic models, are as accurate as full expansion models. Numerical analysis is restricted to closed-form solutions via Naviertype solutions. A number of problems related to laminated and sandwich structures are solved and related reduced models are built by varying geometrical, lay-up and mechanical parameters. Results show that in some cases (in particular those related to sandwich plates) reduced layer-wise models can save up to 50% of the degrees-of-freedom of the full models without significant accuracy losses. It is found that the significant terms related to reduced models are very much subordinated to the problems considered and that from that point of view the use of a framework that can generate any theory, such as CUF, appears very suitable to build reduced models for plates.

The Ritz – Sublaminate Generalized Unified Formulation approach for piezoelectric composite plates

“…The effect of model assumptions on the accuracy can be quantified in a systematic manner with respect to the associated computational cost by referring to the so-called mixed axiomatic/asymptotic approach [37][38][39]: Best Theory Diagrams have been derived in the framework of analytical Navier-type and FEM solutions for sample problems involving homogeneous metallic plates as well as laminated and sandwich plates. This technique has been applied to analytical Navier-type solutions for piezoelectric plates in [40].…”

Evaluation of mixed theories for laminated plates through the axiomatic/asymptotic method

“…The latter sometimes are not very accurate at the top and bottom regions and do not guarantee the transverse stress interlaminar continuity. It must be underlined that LD4 reduced models that can fulfill the top and bottom BCs can be obtained by means of other AAM strategies as shown in [53].…”

“…The BTD is problem-dependent, and it can be obtained by exploiting genetic algorithms [49,50]. The most recent developments have dealt with the definition of more accurate techniques to evaluate the accuracy of the model [51,52], layer-wise plate [53] and shell [54] models.…”

Best Theory Diagrams for cross-ply composite plates using polynomial, trigonometric and exponential thickness expansions

“…This leads to the development of reduced models whose accuracies are equivalent to those of full higher-order models. The AAM has been applied to several problems, including: static and free vibration of beams [38,40], metallic and composite plates [39,41], shells [42,43], LW models [44,45], advanced models based on the Reissner Mixed Variational Theorem [46], and piezoelectric plates [47].…”