New Straightforward Benchmark Solutions for Bending and Free Vibration of Clamped Anisotropic Rectangular Thin Plates

This study presents new straightforward benchmark solutions for bending and free vibration of clamped anisotropic rectangular thin plates by a double finite integral transform method. Being different from the previous studies that took pure trigonometric functions as the integral kernels, the exponential functions are adopted, and the unknowns to be determined are constituted after the integral transform, which overcomes the difficulty in solving the governing higher-order partial differential equations with odd derivatives with respect to both the in-plane coordinate variables, thus goes beyond the limit of conventional finite integral transforms that are only applicable to isotropic or orthotropic plates. The present study provides an easy-to-implement approach for similar complex problems, extending the scope of finite integral transforms with applications to plate problems. The validity of the method and accuracy of the new solutions that can serve as benchmarks are well confirmed by satisfactory comparison with the numerical solutions.

New H 2 O weighted sum of gray gases model for natural convection flows within large cavities

Radiation heat transfer plays a significant role in buoyancy driven flows for large scale facilities. In the analysis of nuclear containment safety during severe accidents, it has been found that the thermal radiation particularly affects the temperature distribution and containment pressurization due to the humidity environment. In order to model thermal radiation, one of the main challenges is the description of nongray gas property for the steam-air mixtures. The weighted sum of gray gases model (WSGG) is a reasonable method in engineering applications because of its computational efficiency. There are many WSGG models available for combustion applications, but none of them is dedicated for low temperature applications. Furthermore, most of the existing WSGG models only provide the fixed partial pressure ratios (e.g., p H 2 O = 2p CO 2 for methane). To overcome this limitation, a tailored WSGG model is derived by the Line-by-Line model for a gas mixture composed of arbitrary concentrations of H 2 O. This tailored WSGG model is valid for the pressure path length ranging from 0.0001 to 10 atm · m, and for the temperature from 300 to 1200 K. The WSGG correlations are verified against the Line-by-Line benchmark solutions with isothermal/non-isothermal temperatures and homogeneous/non-homogeneous concentrations. The results demonstrate the ability and efficiency of the new tailored WSGG formulation.

A Vector Wavenumber Integration Model of Underwater Acoustic Propagation Based on the Matched Interface and Boundary Method

Acoustic particle velocities can provide additional energy flow information of the sound field; thus, the vector acoustic model is attracting increasing attention. In the current study, a vector wavenumber integration (VWI) model was established to provide benchmark solutions of ocean acoustic propagation. The depth-separated wave equation was solved using finite difference (FD) methods with second- and fourth-order accuracy, and the sound source singularity in this equation was treated using the matched interface and boundary method. Moreover, the particle velocity was calculated using the wavenumber integration method, consistent with the calculation of the sound pressure. Furthermore, the VWI model was verified using acoustic test cases of the free acoustic field, the ideal fluid waveguide, the Bucker waveguide, and the Munk waveguide by comparing the solutions of the VWI model, the analytical formula, and the image method. In the free acoustic field case, the errors of the second- and fourth-order FD schemes for solving the depth-separated equation were calculated, and the actual orders of accuracy of the FD schemes were tested. Moreover, the time-averaged sound intensity (TASI) was calculated using the pressure and particle velocity, and the TASI streamlines were traced to visualize the time-independent energy flow in the acoustic field and better understand the distribution of the acoustic transmission loss.

Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

In this work, we discuss the free vibration behavior of thin-walled composite shell structures reinforced with carbon nanotubes (CNTs) in a nonlinear setting and resting on a Winkler–Pasternak Foundation (WPF). The theoretical model and the differential equations associated with the problem account for different distributions of CNTs (with uniform or nonuniform linear patterns), together with the presence of an elastic foundation, and von-Karman type nonlinearities. The basic equations of the problem are solved by using the Galerkin and Grigolyuk methods, in order to determine the frequencies associated with linear and nonlinear free vibrations. The reliability of the proposed methodology is verified against further predictions from the literature. Then, we examine the model for the sensitivity of the vibration response to different input parameters, such as the mechanical properties of the soil, or the nonlinearities and distributions of the reinforcing CNT phase, as useful for design purposes and benchmark solutions for more complicated computational studies on the topic.

Walk the Line: Optimizing the Layout Design of Moving Walkways

A moving walkway (also denoted as moving sidewalk, travelator, autowalk, pedestrian conveyor, or skywalk) is a slow moving conveyor that transports standing or walking people horizontally over a short to medium distance. Constantly moving walkways have a long-lasting tradition especially inside large buildings, such as airport terminals and railway stations. Novel technological developments allow to accelerate walkways in their middle sections up to 12 km/h, while still providing a safe and much slower entrance and exit. Furthermore, first applications of moving walkways as environmentally friendly and space-efficient alternatives for urban public transport exist. In this context, our paper aims to support the layout design of moving walkways with optimization. Given a straight corridor (e.g., an airport terminal) and the passenger flows within the corridor (e.g., among gates), we aim to optimally place bidirectional walkway segments. We show that the resulting optimization problem is efficiently solvable by dynamic programming even if multiple relevant extensions, such as multiple objectives, budget constraints, and minimum safety distances, among subsequent segments are relevant. We apply our algorithm to explore the impact of constantly moving and accelerating walkways on total travel times and benchmark solutions without walkway support in a real-world case study. Our results reveal that wrongly placed walkways may considerably slow down passenger transport, but a very simple design rule leads to near-optimal results.

Simulation-based assessment of coupled frequency response of magneto-electro-elastic auxetic multifunctional structures subjected to various electromagnetic circuits

This article deals with the modeling of magneto-electro-elastic auxetic structures and developing a methodology in COMSOL Multiphysics® to assess the free vibration response of such structures when subjected to various electromagnetic circuit conditions. The triple energy interaction between elastic, magnetic, and electric fields are established in the COMSOL Multiphysics® using structural mechanics and electromagnetic modules. The multiphase magneto-electro-elastic material with different percentages of piezoelectric and piezomagnetic phases are used as the material. In the solid mechanics module, the piezoelectric and piezomagnetic materials were created in stress-charge and stress-magnetization forms, respectively. The electric and magnetic fields are defined in COMSOL Multiphysics® through electromagnetic equations. Further, the customized controlled meshing constituted of free tetrahedral and triangular elements is adapted to trade-off between the accuracy and the computational expenses. The eigenvalue analysis is performed to obtain the natural frequencies of the MEE re-entrant auxetic structures. Also, the efficiency of smart auxetic structures over conventional honeycomb structures is presented throughout the manuscript. In addition, the discrepancy in the natural frequencies of the structures considering coupled and uncoupled state is also illustrated. It is believed that the modeling procedure and its outcomes serve as benchmark solutions for further design and analysis of smart auxetic magneto-electro-elastic structures.

The Modified LS-STAG Method Application for Planar Viscoelastic Flow Computation in a 4:1 Contraction Channel

In this study we present the modification of the LS-STAG immersed boundary cut-cell method. This modification is designed for viscoelastic fluids. Linear and quasilinear viscoelastic fluid models of a rate type are considered. The obtained numerical method is implemented in the LS-STAG software package developed by the author. This software is created for viscous incompressible flows simulation both by the LS-STAG method and by it developed modifications. Besides of this, the software package is designed to compute extra-stresses for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson --- Segalman fluids on the LS-STAG mesh. The construction of convective derivatives discrete analogues is described for Oldroyd, Cotter --- Rivlin, Jaumann --- Zaremba --- Noll derivatives. The centers of base LS-STAG mesh cells are the locations for shear non-Newtonian stresses computation. The corners of these cells are the positions for normal non-Newtonian stresses computation. The first order predictor--corrector scheme is the basis for time-stepping numerical algorithm. Benchmark solutions for the planar flow of Oldroyd-B fluid in a 4:1 contraction channel are presented. A critical value of Weissenberg number is defined. Computational results are in good agreement with the data known in the literature

A dynamic coefficient matrix method for the free vibration of thin rectangular isotropic plates

The free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS and in-house conventional FEM programs using both 12- and 16-DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi-exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two-dimensional structural components during the preliminary design stages, before a detailed design begins.

A dynamic coefficient matrix method for the free vibration of thin rectangular isotropic plates

The free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS and in-house conventional FEM programs using both 12- and 16-DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi-exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two-dimensional structural components during the preliminary design stages, before a detailed design begins.