Multiobjective Best Theory Diagrams for cross-ply composite plates employing polynomial, zig-zag, trigonometric and exponential thickness expansions

TLDR: In this article, the authors present best theory diagrams (BTDs) for plates considering all the displacement and stress components as objectives, a diagram in which the minimum number of terms that have to be used to achieve the desired accuracy can be read Maclaurin, zig-zag, trigonometric and exponential expansions are employed for static analysis of cross-ply composite plates.

About: This article is published in Composite Structures.The article was published on 2017-09-15 and is currently open access. It has received 12 citations till now. The article focuses on the topics: Polynomial.

Figures

Figure 7. Displacement and stress distributions along the thickness, 0º/90º/0º, 𝑎 ℎ⁄ = 20.

Figure 1. Plate geometry and reference system.

Table 12: Comparison between the accuracies of best EDZ4 and EDZ17 models in computing displacement and stress components, 0º/90º, 𝑎 ℎ⁄ = 20.

Figure 6. Displacement and stress distributions along the thickness, 0º/90º/0º, 𝑎 ℎ⁄ = 5.

Table 4: LD4 model assessment for 3-layer and 5-layer laminated plates.

Table 1: Expansion terms of the proposed theories.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Multiobjective best theory diagrams for cross-ply composite plates employing polynomial, zig-zag, trigonometric and exponential thickness expansions" ?

Yarasca et al. this paper proposed a multiobjective best theory diagram for cross-ply composite plates employing polynomial, zig-zag, trigonometric and exponential thickness expansions. 

Q2. What future works have the authors mentioned in the paper "Multiobjective best theory diagrams for cross-ply composite plates employing polynomial, zig-zag, trigonometric and exponential thickness expansions" ?

Future works should tackle the construction of BTDs for dynamic problems. 

Q3. What are the steps of a typical AAM analysis?

A typical AAM analysis has the following steps:(1) Parameters such as geometry, boundary conditions, loadings, materials, andstacking sequences are fixed. 

Q4. What is the main reason for the high demand for the use of composite materials?

The high demand for the use of composite material structures calls for research of efficient and accurate numerical techniques to predict the structural and dynamical behavior of laminated composites. 

Q5. What is the upper limit of the error of each output parameter?

%𝐸𝑟𝑟𝑜𝑟𝑢𝑙 is equal to the sum of the mean error and the standard deviation and is a measure of the upper limit of the error of each output parameter considered. 

Q6. What are the common applications of composite plates?

Composite laminated plates are increasingly common in many engineering applications, such as aerospace, mechanical, marine and civil structures. 

Q7. What is the efficient kinematic model for a given structural problem?

(8) The most efficient kinematic model for a given structural problem is then obtainedby discarding all the noneffective displacement variables. 

Q8. What are the results of the EDZ4 refined models?

Although the EDZ4 refined models are in good agreements with LD4 results forboth length-to-thickness ratios, further improvements can be obtained by adding trigonometric and exponential terms to the plate model. 

Q9. How many terms can be detected in the plate model?

For instance, the plate model of Eq. (19) can detect displacements and stresses with %𝐸𝑟𝑟𝑜𝑟𝑢𝑙 = 0.4302 %, while the plate model of Eq. (20) can detect displacements and stresses with %𝐸𝑟𝑟𝑜𝑟𝑢𝑙 = 0.6112 %. 

Q10. What is the theory diagram for cross-ply laminated plates?

(2) Overall, the addition of trigonometric and exponential terms may improve theaccuracy and computational cost of refined plate theories. 

Q11. Why is the selection of a plate model more complicated than with a single output parameter?

Due to the large number of best plate theories in the Pareto front, the selection of a plate model is still more complicate than the case with a single output parameter. 

Q12. What is the number of unknown variables in the model?

The number of all possible combinations of active/not-active terms for a given model is equal to 2𝑀, where M is the number of unknown variables (DOFs) in the model. 

Q13. What is the purpose of the present work?

The present work presents a method to develop BTDs considering multipleobjectives simultaneously; in particular, the three displacement components and the six stress ones.