In this article, we’ll show how to solve the time-fractional seventh-order Lax’s Korteweg–de Vries and Kaup–Kupershmidt equations analytically using the homotopy perturbation approach, the Adomian decomposition method, and the Elzaki transformation. The KdV equation is a general integrable equation with an inverse scattering transform-based solution that arises in a variety of physical applications, including surface water waves, internal waves in a density stratified fluid, plasma waves, Rossby waves, and magma flow. Fractional derivative is described in the Caputo sense. The solutions to fractional partial differential equation is computed using convergent series. The numerical computations and graphical representations of the analytical results obtained using the homotopy perturbation and decomposition techniques. Moreover, plots that are simple to grasp are used to compare the integer order and fractional-order solutions. After only a few iterations, we may easily obtain numerical results that provide us better approximations. The exact solutions and the derived solutions were observed to be very similar. The suggested methods have also acquired the highest level of accuracy. The most prevalent and convergent techniques for resolving nonlinear fractional-order partial differential issues are the applied techniques.

Wire ropes are widely observed in many industries such as marine engineering and civil engineering, as a type of structure that can bear huge axial force. There are various kinds of wire ropes in practical engineering, corresponding to different usage scenarios. This paper focuses on 6 × 36SW + 1WR with a diameter of 16 mm. The axial mechanical properties of the wire rope are investigated by experimental, theoretical, and numerical methods. The stress–strain curve and ultimate strength of the steel wire rope obtained in the test are compared with the corresponding results from the finite element simulation. The comparison demonstrates the accuracy and reliability of the finite element model. In addition, a series of parametric studies are conducted to investigate the influence of pitch length and friction coefficient, etc. The purpose of this paper is to propose an accurate and efficient finite element model for the mechanical analysis of wire ropes.

Composite structures, such as the fiberglass reinforced structure studied in this paper, have been normally treated in previous research as homogeneous anisotropic laminated plates regarding the investigation of their mechanical properties. Throughout this paper, this specific structure is considered in a different way in which the fiberglass and polyethylene matrix are treated separately. By using the proposed method, the material plasticity of polyethylene and the fracture stress of the fiberglass can be taken into account, and thus the fracture of the fiberglass inside the fiberglass reinforced flexible pipes(FGRFP) can be predicted. The mechanical behaviour behavior of FGRFP under two real-life main loadings(tension and internal pressure) is investigated by using analytical and numerical methods based on the proposed technique. Experiments are used to verify the results.

A numerical model in slice configuration was applied to the Central Andaman Sea in order to derive metocean operational and design criteria associated to internal solitary waves which are large amplitude interfacial waves. For that purpose, a 10 year hindcast was generated. The model was driven by tides at the open boundary and included realistic stratification and topogra-phy. The results have been compared to data mostly taken from satellites and proved to be accurate in determining parameters such as phase speed and interpacket distance. The phase speeds range from 2.21 m/s in March to 2.5 m/s in November. Corresponding interpacket distances range from 99 km to 111 km in close agreement with available data. According to the model results internal solitary waves are more/less frequent in March/August. Model outputs were specifically analyzed at 2 arbi-trary locations. Maximum current speeds obtained with the model at those locations occur in November reaching a value close to 1.5 m/s. The computed velocities associated to return periods of 1, 10, 50, 100 and 1000 years are, respectively, 1.67 m/s, 1.76 m/s, 1.8 m/s, 1.81 m/s and 1.84 m/s.