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Reducing aircraft fuel consumption has become a paramount research area, focusing on optimizing operational parameters like speed and altitude during the cruise phase. However, the existing methods for fuel reduction often rely on complex experimental calculations and data extraction from embedded systems, making practical implementation challenging. To address this, this study aims to devise a simple and accessible approach using available information.

In this paper, a novel analytic method to estimate and optimize fuel consumption for aircraft equipped with jet engines is proposed, with a particular emphasis on speed and altitude parameters. The dynamic variations in weight caused by fuel consumption during flight are also accounted for. The derived fuel consumption equation was rigorously validated by applying it to the Boeing 737–700 and comparing the results against the fuel consumption reference tables provided in the Boeing manual. Remarkably, the equation yielded closely aligned outcomes across various altitudes studied. In the second part of this paper, a pioneering approach is introduced by leveraging the particle swarm optimization algorithm (PSO). This novel application of PSO allows us to explore the equation’s potential in finding the optimal altitude and speed for an actual flight from Algiers to Brussels.

The results demonstrate that using the main findings of this study, including the innovative equation and the application of PSO, significantly simplifies and expedites the process of determining the ideal parameters, showcasing the practical applicability of the approach.

The suggested methodology stands out for its simplicity and practicality, particularly when compared to alternative approaches, owing to the ready availability of data for utilization. Nevertheless, its applicability is limited in scenarios where zero wind effects are a prevailing factor.

The research opens up new possibilities for fuel-efficient aviation, with a particular focus on the development of a unique fuel consumption equation and the pioneering use of the PSO algorithm for optimizing flight parameters. This study’s accessible approach can pave the way for more environmentally conscious and economical flight operations.

A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues.

Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions.

In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems.

To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions.