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Based on the error analysis, the authors proposed a new kind of high accuracy boundary element method (BEM) (HABEM), and for the large-scale problems, the fast algorithm, such as adaptive cross approximation (ACA) with generalized minimal residual (GMRES) is introduced to develop the high performance BEM (HPBEM). It is found that for slender beams, the stress analysis using iterative solver GMRES will difficult to converge. For the analysis of slender beams and thin structures, to enhance the efficiency of GMRES solver becomes a key problem in the development of the HPBEM. The purpose of this paper is study on the preconditioning method to solve this convergence problem, and it is started from the 2D BE analysis of slender beams.

The conventional sparse approximate inverse (SAI) based on adjacent nodes is modified to that based on adjacent nodes along the boundary line. In addition, the authors proposed a dual node variable merging (DNVM) preprocessing for slender thin-plate beams. As benchmark problems, the pure bending of thin-plate beam and the local stress analysis (LSA) of real thin-plate cantilever beam are applied to verify the effect of these two preconditioning method.

For the LSA of real thin-plate cantilever beams, as GMRES (m) without preconditioning applied, it is difficult to converge provided the length to height ratio greater than 50. Even with the preconditioner SAI or DNVM, it is also difficult to obtain the converged results. For the slender real beams, the iteration of GMRES (m) with SAI or DNVM stopped at wrong deformation state, and the computation failed. By changing zero initial solution to the analytical displacement solution of conventional beam theory, GMRES (m) with SAI or DNVM will not be stopped at wrong deformation state, but the stress error is still difficult to converge. However, by GMRES (m) combined with both SAI and DNVM preconditioning, the computation efficiency enhanced significantly.

This paper presents two preconditioners: DNVM and a modified SAI based on adjacent nodes along the boundary line of slender thin-plate beam. In the LSA, by using GMRES (m) combined with both DNVM and SAI, the computation efficiency enhanced significantly. It provides a reference for the further development of the 3D HPBEM in the LSA of real beam, plate and shell structures.

The strength and stiffness of steel deteriorate rapidly at elevated temperatures. Thus, the characteristics of steel structures exposed to fire have been concerned in recent years. Most studies on the fire response of steel structures were conducted at uniformly distributed temperatures. This study aims to evaluate the buckling capacity of steel H-beams subjected to different loading conditions under non-uniform heating.

A numerical investigation was conducted employing finite element analysis software, ABAQUS. A comparison between the numerical analysis results and the experimental data from previous studies was conducted to verify the beam model. Simply supported beams were loaded with several loading conditions including one end moment, end equal moments, uniformly distributed load and concentrated load at midspan. The effects of initial imperfections were considered. The buckling capacities of steel beams under fire using the existing fire design code and the previous study were also generated and compared.

The results showed that the length-to-height ratio and loading conditions have a great effect on the buckling resistance of steel beams under fire. The capacity of steel beams under non-uniform temperature distribution using the existing fire design code and the previous study can give unconservative values or too conservative values depending on loading conditions. The maximum differences of unconservative and conservative values are −44.5 and 129.2% for beams subjected to end equal moments and one end moment, respectively.

This study provides the buckling characteristics of steel beams under non-uniform temperature considering the influences of initial imperfections, length-to-height ratios, and loading conditions. This study will be beneficial for structural engineers in properly evaluating structures under non-uniform heating conditions.

For flow around elongated bluff bodies, flow separations would occur over both leading and trailing edges. Interactions between these two separations can be established through acoustic perturbation. In this paper, the flow and the acoustic fields of a D-shaped bluff body (length-to-height ratio L/H = 3.64) are investigated at height-based Reynolds number Re = 23,000 by experimental and numerical methods. The purpose of this paper is to study the acoustic feedback in the interaction of these two separated flows.

The flow field is measured by particle image velocimetry, hotwire velocimetry and surface oil flow visualization. The acoustic field is modeled in two dimensions by direct aeroacoustic simulation, which solves the compressible Navier–Stokes equations. The simulation is validated against the experimental results.

Separations occur at both the leading and the trailing edges. The leading-edge separation point and the reattaching flow oscillate in accordance with the trailing-edge vortex shedding. Significant pressure waves are generated at the trailing edge by the vortex shedding rather than the leading-edge vortices. Pressure-based cross-correlation analysis is conducted to clarify the effect of the pressure waves on the leading-edge flow structures.

The understanding of interactions of separated flows over elongated bluff bodies helps to predict aerodynamic drag, structural vibration and noise in engineering applications, such as the aerodynamics of buildings, bridges and road vehicles.

This paper clarifies the influence of acoustic perturbations in the interaction of separated flows over a D-shaped bluff body. The contribution of the leading- and the trailing-edge vortex in generating acoustic perturbations is investigated as well.

The purpose of this study is to investigate the influence of enclosure shape on magnetohydrodynamic (MHD) nanofluidic flow, heat transfer and irreversibility in square, trapezoidal and triangular thermal systems under fluid volume constraints, with the aim of optimizing thermal behavior in diverse applications.

The study uses numerical simulations based on a finite element-based technique to analyze the effects of the Rayleigh number (Ra), Hartmann number (Ha), magnetic field orientation (γ) and nanoparticle concentration (ζ) on heat transfer characteristics and thermodynamic entropy production.

The key findings reveal that the geometrical design significantly influences fluid velocity, heat transfer and irreversibility. Trapezoidal thermal systems outperform square systems, while triangular systems achieve optimal enhancement. Nanoparticle concentration enhances heat transfer and flow strength at higher Rayleigh numbers. The magnetic field intensity has a significant impact on fluid flow and heat transport in natural convection, with higher Hartmann numbers resulting in reduced flow strength and heat transfer. The study also highlights the influence of various parameters on thermodynamic entropy production.

Further research can explore additional geometries, parameters and boundary conditions to expand the understanding of enclosure shape effects on MHD nanofluidic flow and heat transfer. Experimental validation can complement the numerical simulations presented in this study.

This study provides valuable insights into the impact of enclosure shape on heat transfer performance in MHD nanofluid flow systems. The findings contribute to the optimization of thermal behavior in applications such as electronics cooling and energy systems. The comparison of different enclosure shapes and the analysis of thermodynamic entropy production add novelty to the study.

The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column.

The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation.

An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated.

The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.

The purpose of this study is to propose generalised integral transform technique (GITT) to obtain the exact solutions for bending of clamped parallelogram plate resting on elastic foundation.

The GITT is used to solve the bending problem of the full clamped parallelogram plate under an elastic foundation. The auxiliary problem was developed and the corresponding eigenfunction and eigenvalue were calculated simultaneously. The original partial differential governed equation has been represented by the transformed ordinary differential equation system and solved by the subroutine DBVPFD from International Mathematics and Statistics Library.

The GITT has been proven to be an efficient approach to solve the bending problem of the plate with different loads, boundary conditions and elastic foundations. The parametric study indicates that the elastic foundation modulus has significant contribution in reducing the vertical deflections and moments for both rectangular and parallelogram plates. With the increasing of aspect ratio (a/b) and the elastic foundation modulus, the trends of the deflection and moment reduction decreased significantly.

The present hybrid analytical-numerical methodology was first used to solve the mechanics problem of the clamped parallelogram plate resting on elastic foundation. Excellent convergence and high accuracy was observed by comparing with the published results. It exhibits potential application to investigate the mechanics problem of the composite plate with different boundary conditions in the shipbuilding and civil engineering.

The purpose of this paper is to solve the problem of a three-dimensional computational analysis for an elliptic-shaped cavity in a pipe under constant temperature.

The three-dimensional computational solution of governing equations was performed by using finite volume method with different temperature difference.

The parafin wax was chosen as a phase change material (PCM), and melting fraction, streamlines and isotherms are formed for different time step. It is found that position B give better results than that of position A, and temperature difference effects the duration of melting of PCM.

The three-dimensional analysis of melting in an ellipsoidal pipe with inner pipe with higher temperature is the main originality of this work.

This paper aims to simulate the nanofluid forced convection in a microchannel. According to the results, at high Reynolds numbers and higher nanofluid volume fractions, an increase in the rib height and slip coefficient further improved the heat transfer rate. The ribs also affect the flow physics depending on the Reynolds number so that the slip velocity decreases with increasing the nanofluid volume fraction and rib height.

Forced heat transfer of the water–copper nanofluid is numerically studied in a two dimensional microchannel. The effects of the slip coefficient, Reynolds number, nanofluid volume fraction and rib height are investigated on the average Nusselt number, slip velocity on the microchannel wall and the performance evaluation criterion.

In contrast, the slip velocity increases with increasing the Reynolds number and slip coefficient. Afterwards, a non-parametric function estimation is performed relying on the artificial neural network.

Finally, the Genetic Algorithm was used to establish a set of optimal decision parameters for the problem

A numerical study of a two‐dimensional turbulent flow in a partially open rectangular cavity such as a room is carried out. The turbulent flow is induced by the energy input due to a localized heat source positioned on the floor of the cavity. This flow is of interest in enclosure fires where the flow in the cavity interacts with the environment through the opening or vents. The focus is on the stable, thermal stratification that arises in the room and on the influence of the opening height. A finite‐difference method is employed for the solution of the problem, using a low Reynolds number k — ε turbulence model for the turbulent flow calculations. This model is particularly suitable for flows in which the possibility for relaminarization exists. It was found that, for high Grashof numbers and for relatively small opening heights, particularly for doorway openings, a strong stable thermal stratification is generated within the cavity, with a cooler, essentially uniform, layer underlying a warmer, linearly stratified, upper layer. As a consequence, turbulence is suppressed and the flow in the upper region of the cavity becomes laminar with turbulence confined to locations such as the fire plume above the source and the shear layer at the opening. The penetration distance and the height of the interface are both found to decrease with a reduction in the opening height. The Nusselt number for heat transfer from the source is seen to be affected to a small extent by the opening height. The basic trends are found to agree with those observed in typical compartment fires. Comparisons with results available in the literature on turbulent buoyancy‐driven enclosure flows indicate good agreement, lending support to this model and the numerical scheme.

The purpose of this paper is to present a fast and bare bones implementation of a numerical method for quickly simulating turbulent thermal flows on GPUs. The work also validates earlier research showing that the lattice Boltzmann method (LBM) method is suitable for complex thermal flows.

A dual lattice hydrodynamic (D3Q27) thermal (D3Q7) multiple-relaxation time LBM model capable of thermal DNS calculations is implemented in CUDA.

The model has the same computational performance compared to earlier publications of similar LBM solvers. The solver is validated against three benchmark cases for turbulent thermal flow with available data and is shown to be in excellent agreement.

The combination of a D3Q27 and D3Q7 stencil for a multiple relaxation time -LBM has, to the authors’ knowledge, not been used for simulations of thermal flows. The code is made available in a public repository under a free license.