In this paper, we prove that F iterative scheme is almost stable for weak contractions. Further, we prove convergence results for weak contractions as well as for generalized non-expansive mappings due to Hardy and Rogers via F iterative scheme. We also prove that F iterative scheme converges faster than the some known iterative schemes for weak contractions. An illuminative numerical example is formulated

The heat transfer and flow attributes of a cylindrical microchannel heat sink (CMCHS) operated with a hybrid nanofluid containing the graphene nanoplatelets and platinum particles are numerically investigated. The CMCHS is modeled with three different numbers of fins, and the problem is solved for four concentrations and four Reynolds numbers. The effect of these variables on the thermal and frictional

In this paper, a localized radial basis function (RBF) method is applied to obtain a global approximation of the solution of two dimensional Klein-Gordon equation on a given bounded domain. We use the RBF partition of unity (RBF-PU) method which is based on partitioning the original domain to several patches and using the RBF approximation on each local domain. Low computational cost and well conditioned

Making a relation between strains and stresses is an important subject in the rock engineering field. Shear behaviors of rock fractures have been extensively investigated by different researchers. Literature mostly consists of constitutive models in the form of empirical functions that represent experimental data using mathematical regression techniques. As an alternative, this study aims to present

In the present paper, a new trigonometric two-variable shear deformation beam nonlocal strain gradient theory is developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending, buckling and free vibration analysis of nanobeams. The model introduces a nonlocal stress field parameter and a length scale parameter to capture the size effect. The governing

Wave propagation simulation in a multi-hybrid nanocomposite (MHC)-reinforced doubly curved open shell covered with piezoelectric actuator is examined for the first time. The third-order shear deformation theory (third-order SDT) is applied to formulate the stress–strain relations. Rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constants of the MHC-reinforced

In the present study, two-phase flow and forced-convection heat transfer of hydrogen gas (H2) in a solar finned and baffled channel heat exchanger (SFBCHE) is studied numerically. The effect of different obstacles in the channel is addressed. A H2 heat transfer fluid (HTF) having a high thermal conductivity with the baffling technique is implemented to enhance the overall performance of a solar channel

This paper deals with dynamic stability of functionally graded (FG) nanocomposite annular plate reinforced with graphene platelets (GPLs) subjected to a periodic radial compressive load in thermal environment. On the basis of modified Halpin–Tsai micromechanics model, the effective elastic modulus of structure is estimated. Taking into consideration of the first-order shear deformation theory, the

This study investigates the search capability, stability, and computational efficiency of four improved penalty-free constraint-handling techniques (CHTs), including the death penalty, the Deb rule, the filter method, and the mapping strategy, in structural optimization using harmony search (HS). The first three general-purpose CHTs have been improved by hybridizing with a structural analysis filter

This paper investigates the linear stability of the flow in the two-dimensional boundary-layer flow of the Carreau fluid over a wedge. The corresponding rheology is analysed using the non-Newtonian Carreau fluid. Both mainstream and wedge velocities are approximated in terms of the power of distance from the leading edge of the boundary layer. These forms exhibit a class of similarity flows for the

This paper presents the free vibration and buckling analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) laminated non-rectangular plates, i.e., quadrilateral and skew plates, using a four-nodded straight-sided transformation method. At first, the related equations of motion and buckling of quadrilateral plate have been given, and then, these equations are transformed from the irregular

In this paper, we present a novel approach to attain fourth-order approximate solution of 2D quasi-linear elliptic partial differential equation on an irrational domain. In this approach, we use nine grid points with dissimilar mesh in a single compact cell. We also discuss appropriate fourth-order numerical methods for the solution of the normal derivatives on a dissimilar mesh. The method has been

The radial basis function method for 3D advection diffusion reaction equations with variable coefficients is presented. The proposed method implements the linear combination of radial basis functions which impose boundary conditions in advance, and thus such a combination with weighted parameters can be used to construct the final approximation. Furthermore, the weighted parameters are solved by substituting

We study a new sixth-order compact discretization using uniform three-grid point for the mildly nonlinear differential equation \(\phi ''=g(t,\phi )\), subject to the values of ϕ given at two end points of the regular solution interval. We also discuss three-step AGE (THAGE) iteration method as an application to the resulting difference equation as a powerful numerical computation device. In this algorithm

Accurate prediction of the liquefaction-induced settlement (\({S}_{\mathrm{lc}}\)) is an essential requirement for a good design of buildings resting on liquefiable ground and subjected to seismic shake. However, prediction of the \({S}_{\mathrm{lc}}\) is not straightforward process and it requires advanced soil models and calibrated soil parameters that are not readily available for designers/practitioners

This article aims to present comprehensive model and analytical solution to investigate the static bending behavior of regularly squared cutout perforated thin/thick nanobeams incorporating the coupled effect of the microstructure and surface energy for the first time. The perforation influence is considered to be deriving equivalent geometrical and material characteristics. The modified couple stress

The static bending behavior of porous functionally graded (PFG) micro-plate under the geometrically nonlinear analysis is studied in this article. A small-scale nonlinear solution is established using the Von-Kármán hypothesis and the modified couple stress theory (MCST). To obtain the deflection of the plate, the Reddy higher-order plate theory coupled with isogeometric analysis (IGA) is utilized

In this paper, a novel trust-region-based surrogate-assisted optimization method, called CBOILA (Constrained Black-box Optimization by Intrinsically Linear Approximation), has been proposed to reduce the number of black-box function evaluations and enhance the efficient performance for solving complex optimization problems. This developed optimization approach utilizes an assembly of intrinsically

In this paper, we propose an efficient numerical technique based on the Bernstein polynomials for the numerical solution of the equivalent integral form of the derivative dependent Emden–Fowler boundary value problems which arises in various fields of applied mathematics, physical and chemical sciences. The Bernstein collocation method is used to convert the integral equation into a system of nonlinear

The occurrence of unpredictable hazards are frequent with the increased depth of mining, especially the hazards caused by stress concentration. In order to mitigate the negative effectiveness results from mining-induce stress, various approaches have been employed in underground mines. Destress blasting, as an efficient method, has gained a lot of popularity in recent years. However, it is crucial

This paper presents a fully Lagrangian mixed discrete least squares meshfree (MDLSM) method for simulating the free surface problems. In the proposed method, the mass and momentum conservation equations are first discretized in time using the projection method. The resulting pressure Poisson equation is then re-written in the form of three first-order equations in terms of the pressure field and its

The analysis of the wave propagation behavior of a sandwich structure with a soft core and multi-hybrid nanocomposite (MHC) face sheets is carried out in the framework of the higher-order shear deformation theory (HSDT). In order to take into account the viscoelastic influence, the Kelvin-Voight model is presented. In this paper, the constituent material of the core is made of an epoxy matrix which

In this study, we present an alternative finite element to multiscale analysis. In this strategy, strain energy comes only from semi-discrete or lattice elements immersed in a continuum without stiffness, enabling mechanical analysis from molecular scales to macroscopic scales. Some characteristics of the proposed element are: (1) geometrically non-linear exact description that allows the presence

Using surrogate models to substitute the computationally expensive limit state functions is a promising way to decrease the cost of implementing reliability-based design optimization (RBDO). To train the models efficiently, the active learning strategies have been intensively studied. However, the existing learning strategies either do not individually build the models according to importance measurement

The sample distribution has a vital influence on the quality of a Kriging surrogate model, which may further influence the required cost or convergence of the surrogate model-based design and optimization problems. Adaptive sampling methods utilize the information from existing samples to reasonably allocate the sequential samples, which can generally build a more accurate Kriging surrogate model under

Because of fasttechnological development, electrostatic nanoactuator devices like nanosensors, nanoswitches, and nanoresonators are highly considered by scientific community. Thus, this article presents a new solution technique in solving highly nonlinear integro-differential equation governing electrically actuated nanobeams made of functionally graded material. The modified couple stress theory and

The present paper suggests an equation for the average contact number of carbon nanotubes (CNTs) in CNT-reinforced polymer nanocomposites (PCNT) by two developed equations for electrical conductivity. Several novel parameters in PCNT such as CNT size, CNT concentration, network fraction, interphase depth, tunneling effect, and CNT wettability by the polymer medium are considered to define the average

In this article, mixed element algorithms with second-order time convergence results for the two-dimensional time fractional Maxwell’s equations in the Cole–Cole dispersive medium are developed. Fully discrete mixed element systems with shifted parameters \(\theta\) at time \(t=t_{n-\theta }\), which are constructed by combining the generalized BDF2-\(\theta\) schemes in temporal direction and a mixed

A new technique based on beta functions is applied to compute the exact formula for the Riemann–Liouville fractional integral of the fractional-order generalized Chelyshkov wavelets. An approximation method based on the wavelets is proposed to effectively solve nonlinear fractional differential equations. Illustrative examples show that the proposed method gives solutions with less errors in comparison

In this research, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the multi-scale hybrid nano-composite reinforced disk in the thermal environment and subject to a harmonic external load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution

Integro-differential equations are developed as models in enormous fields of engineering and science such as biological models, population growth, aerospace systems and industrial mathematics. In this work, we consider a general class of nonlinear fractional integro-differential equations with variable order derivative. We use the operational matrices based on the Bernstein polynomials to obtain numerical

This article presents a nonlinear displacement based finite elements model to study and analyze the nonlinear dynamic response of flexible double wishbone structural vehicle suspension system considering damping effect which was not previously discussed elsewhere. Due to large deflection and moderate rotation encountered during passing over road bumps, the kinematic nonlinearity is included through

This study contains numerical schemes namely Linear scheme, Quadratic scheme, and Quadratic–linear scheme to solve a fractional integro-differential equation using the Atangana–Baleanu derivative defined in Caputo sense. The error bounds of the schemes are obtained. We discuss four test examples to perform the numerical simulations, and the obtained numerical results ensure that the presented schemes

A new numerical learning approach namely Rational Gegenbauer Least Squares Support Vector Machines (RG_LS_SVM), is introduced in this paper. RG_LS_SVM method is a combination of collocation method based on rational Gegenbauer functions and LS_SVM method. This method converts a nonlinear high order model on a semi-infinite domain to a set of linear/nonlinear equations with equality constraints which

The crucial significance of proper management of heating, ventilating, and air conditioning systems in energy-efficient buildings were the main reason for dedicating this study to test a novel approach for this task. Shuffled complex evolution (SCE) is an efficient metaheuristic technique that is used to optimize the performance of a multi-layer perceptron neural network (MLP) for accurate prediction

In the present work, the characteristics of physical model unsteady nanofluid flow and heat transfer in an asymmetric porous channel are analyzed numerically using wavelet collocation method. Using similarity transformation, unsteady two-dimensional flow model of nanofluid in a porous channel through expanding or contracting walls has been transformed into a system of nonlinear ordinary differential

The main propose of this investigation is to develop an interpolating meshless numerical procedure for solving the stochastic parabolic interface problems. The present numerical algorithm is constructed from the interpolating moving least squares (ISMLS) approximation. At first, the space variable has been discretized by using the ISMLS approximation. Then, the PDE reduces to the system of nonlinear

In the current work, the dynamic behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate with negative Poisson’s ratio (NPR) is investigated by combining higher-order shear deformation theory and large deflection theory. First, explicit solutions are proposed to predict the effective Poisson’s ratio (EPR) of the laminates. Taking carbon nanotube-reinforced composite (CNTRC)

The numerical investigation is performed on the vibration of the higher order shear deformable carbon nanotube reinforced composite (CNTRC) spherical panels subjected to the initial external pressure. The functionally graded nanocomposite is reinforced with the non-uniform distribution of CNTs. The problem is formulated following the higher order shear deformation shell theory (HSDT) within the variational

The relevance vector machine (RVM) is considered a robust machine learning method and its superior performance has been confirmed through many successful engineering applications. To improve the performance of the RVM model, three single kernel functions, and three multikernel functions, including two newly proposed multikernel functions, tenfold cross-validation, and the hybrid particle swarm optimization

Existing reliability analyses of embankment slopes usually considered the spatial variabilities of shear strength parameters and saturated hydraulic conductivity separately. Additionally, the variability in the soil–water characteristic curve (SWCC) was ignored. A non-intrusive approach is proposed for reliability analyses of unsaturated embankment slopes under four different cases on a steady-state

In this paper, we have developed an radial basis function (RBF) based meshless method to solve the time-fractional mixed diffusion and diffusion-wave equation which involves two fractional Caputo derivatives of order \(\alpha \in (0,1)\) and \(\beta \in (1,2)\). The unconditional stability of the proposed numerical scheme is discussed and proved theoretically. The time semi discretization has been

The design and sustainability of reinforced concrete deep beam are still the main issues in the sector of structural engineering despite the existence of modern advancements in this area. Proper understanding of shear stress characteristics can assist in providing safer design and prevent failure in deep beams which consequently lead to saving lives and properties. In this investigation, a new intelligent

The efficiency as computational efforts and accuracy as optimum design condition are two major changes in hybrid intelligent optimization methods for hierarchical stiffened shells (HSS). In this current work, a novel hybrid optimization coupled by adaptive modeling framework is proposed to improve the accuracy of the predicted optimum results of load-carrying capacity for HSS by combining active Kriging

In this paper we make two new lopsided methods (LTSCSP1 and LTSCSP2) based on the two-scale-splitting (TSCSP) method and show that the convergence speed of TSCSP iteration method can be increased under some conditions without adding any additional parameter. The convergence analysis of the new methods in detail is given. Then we will obtain the quasi-optimal parameter to minimize the spectral radius

This paper introduces a new stochastic bio-inspired optimization algorithm, denoted as seasons optimization (SO) algorithm. This algorithm is inspired by the growth cycle of trees in different seasons of a year. It is an iterative and population-based algorithm working with a population of initial solutions known as a forest. Each individual in the forest is referred to as a tree. Until the termination

The geomechanical properties of rock, including shear strength (SS) and uniaxial compressive strength (UCS), are very important parameters in designing rock structures. To improve the accuracy of SS and UCS prediction, this study presented an evolving support vector regression (SVR) using Grey Wolf optimization (GWO). To examine the feasibility and applicability of the SVR-GWO model, the differential

In this paper, the Chebyshev–Gauss–Lobatto collocation method is developed for studying the variable-order (VO) time fractional model of the generalized Hirota–Satsuma coupled KdV system arising in interaction of long waves. To define this new system, the Atangana–Baleanu fractional operator is implemented. The operational matrix of VO fractional differentiation for the shifted Chebyshev polynomials

As a first attempt, the vibration and stability analysis of magnetically embedded spinning axially functionally graded (AFG) nanotubes conveying fluid under axial loads is performed based on the nonlocal strain gradient theory (NSGT). A detailed parametric investigation is conducted to elucidate the influence of key factors such as material distribution type and size-dependent parameters on the divergence

In this research, we study the thermal buckling performance of multi-scale hybrid laminated nanocomposite (MHLC) disk (MHLCD) subjected hygro-mechanical loading. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macro-scale, respectively. The disk is modeled based on higher order shear deformation theory. We present a modified Halpin–Tsai model to

In this study, to overcome the limitations of non-singular fractional derivatives in the Caputo–Fabrizio and Atangana–Baleanu senses (especially in dealing with the variable-order (VO) fractional calculus), we introduce a new non-singular VO fractional derivative with Mittag–Leffler function as its kernel. Some useful results are derived from this fractional derivative. Moreover, this fractional derivative

The bat algorithm (BA) is one of prominent swarm-based algorithm that has the suitability in solving only small dimension engineering problems and suffers from drawback of getting trapped in local minimum with slow convergence for multi-dimensional problems. In the context of improving its applicability in solving large scale and constrained engineering design problems, this paper presents a novel

Laminated composite structures performance and behavior can be affected by damage that is not always visible on the surface. The need to monitor the health of these structures has continuously increased, which can be achieved in a fast and cost-effective way by numerical simulations. This paper presents an efficient two-step approach for damage identification in laminated composite plates. The first

In the current report, characteristics of the propagated wave in a sandwich structure with a soft core and multi-hybrid nanocomposite (MHC) face sheets are investigated. The higher-order shear deformable theory (HSDT) is applied to formulate the stresses and strains. Rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the multi-hybrid nanocomposite

Dynamic coefficient as an important parameter in determination of the dynamic behavior of capillary pressure is considered as a function of various fluid and porous media properties. In this study, a new and general formulation for predicting the dynamic coefficient was proposed and developed through which the key fluid and porous media properties are accounted for. For expressing new formulation,

In this paper, a novel time-marching procedure is proposed for dynamic analysis. The proposed new technique is fourth-order accurate for undamped models; third-order accurate for numerically damped models; and second-order accurate for physically damped models. The method is very straightforward to implement and to apply, allowing providing higher-order accurate time-domain solutions taking into account

Recent improvements achieved using nature-inspired optimizers encouraged the authors to employ a novel type of metaheuristic algorithms, namely crow search algorithm (CSA) in this study. The CSA is employed for optimizing a feed-forward artificial neural network (ANN) in predicting the soil compression coefficient (SCC). The SCC is one of the most crucial geotechnical parameters that the early prediction

Optimization methods are widely used to improve industrial processes and enhance the quality characteristics of product, where process costs are directly linked. Given this assumption, this study aims to present a multivariate proposal of the Taguchi loss function, to model and optimize manufacturing processes, searching to establish values that prioritize quality and provide the minimum loss in view

Optimization algorithms have made considerable advancements in solving complex problems with the ability to be applied to innumerable real-world problems. Nevertheless, they are passed through several challenges comprising of equilibrium between exploration and exploitation capabilities, and departure from local optimums. Portioning the population into several sub-populations is a robust technique

In this article, thermal buckling and resonance frequency of a composite cylindrical nanoshell reinforced with graphene nanoplatelets (GNP) under bi-directional thermal loading are presented. The temperature-dependent material properties of piece-wise GNP-reinforced composites (GNPRC) are assumed to be graded in the thickness direction of a cylindrical nanoshell. Also, Halphin-Tsai nanomechanical model