Homogeneous Plate Research Articles

Boundary and interface methods for energy stable finite difference discretizations of the dynamic beam equation

We consider energy stable summation by parts finite difference methods (SBP-FD) for the homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the constant coefficient problem has been solved with SBP-FD together with penalty terms (SBP-SAT) to impose boundary conditions. In this work, we revisit this problem and compare SBP-SAT to the projection method (SBP-P). We also consider the DBE with discontinuous coefficients and present novel SBP-SAT, SBP-P, and hybrid SBP-SAT-P discretizations for imposing interface conditions. To demonstrate the methodology for two-dimensional problems, we also present a discretization of the piecewise homogeneous dynamic Kirchoff-Love plate equation based on the hybrid SBP-SAT-P method. Numerical experiments show that all methods considered are similar in terms of accuracy, but that SBP-P can be more computationally efficient (less restrictive time step requirement for explicit time integration methods) for both the constant and piecewise constant coefficient problems.

A BRIEF OVERVIEW OF STATIONARY TWO-DIMENSIONAL THERMOELASTIC STATE MODELS IN HOMOGENEOUS AND PIECEWISE-HOMOGENEOUS BODIES WITH CRACKS

Purpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks. Methodology. Based on the method of the function of a complex variable we have studied the two-dimensional thermoelastic state for the body with crack as stress concentrators. As result, the problem of thermoelasticity was reduced to a system of two singular integral equations (SIE) of the first and second kind, a numerical solution of which was found by the method of mechanical quadratures. Findings. The two-dimensional mathematical model of the thermoelastic state has been built in order to determine the stress intensity factors at the top of the crack and inclusion. The systems of singular integral equations of the first and second kinds of the specified problem on closed (contour of inclusion) and open (crack) contours are constructed. The influence of thermophysical and mechanical properties of inclusion on the SIF sat the crack types was investigated. The dependences of the stress intensity factor which characterizes the distribution of the intensity of stresses at the vertices of a crack have been built, as well as its elastic and thermoelastic characteristics of inclusion. This would make it possible to analyze the intensity of stresses in the neighborhoods of crack vertices depending on the geometrical and mechanical factors. As a result, this allows to determine the critical values of temperature in the three-component plate containing a crack in order to prevent the growth of the crack, as well as to prevent the local destruction of the body. It was found that the appropriate selection of mechanical and thermophysical characteristics of the components of a three-component plate containing a crack can be useful to achieve an improvement in body strength in terms of the mechanics of destruction by reducing stress intensity factors at the crack’s vertices. Originality. The solutions of the new two-dimensional problem of thermoelasticity for a specified region due to the action of constant temperature as well as due to local heating by a heat flux were obtained. The studied model is the generalization of the previous models to determine the two-dimensional thermoelastic state in a piecewise homogeneous plate weakened by internal cracks. Practical value. The practical application of this model is a more complete description of the stress-strain state in piecewise homogeneous structural elements with cracks operating under temperature loads. The results of numerical calculations obtained from the solution of systems of equations and presented in the form of graphs can be used in the design of rational modes of operation of structural elements. This takes into account the possibility of preventing the growth of cracks by the appropriate selection of composite components with appropriate mechanical characteristics.

Mathematical Model of the On-Board Antenna of Reentry Spacecraft Taking into Account Surface Waves

Introduction. The onboard antennas of the returned hypersonic aircraft are weakly directional, which is achieved by radiation from the open end of the waveguide. When passing through dense layers of the atmosphere, they are exposed to aerodynamic heating, for protection from which a heat-resistant radio-transparent thermal protection is used. The case of uniform thermal protection of the antenna can be interpreted as the absence of heating or heating uniform in the thickness of the thermal protection.Aim. The problem of obtaining an analytical description of the radiation characteristics of a circular waveguide closed by a flat homogeneous dielectric plate is solved. Since in such a formulation it is necessary to consider the resonant domain, a strict solution of Maxwell's equations is required.Materials and methods. Of the known analytical methods of solution, it is possible to use the method of integral transformations and the method of eigen functions. Both of these methods are used in the work. In this case, the assumption is used that the electrical parameters of the dielectric plate (thermal protection) and the geometric dimensions do not depend on time.Results. The relations describing the directional pattern of a circular waveguide with dielectric thermal protection and taking into account the electrical parameters of thermal protection and its thickness are obtained. Expressions are also obtained for the fields of lateral, surface and outflow waves, from which it is possible to calculate the power output by these fields. Relations for the separation of singular points of integrand expressions into poles corresponding to surface, outflow and lateral waves are obtained. Surface, outflow and lateral waves can have a certain effect on the radiation pattern. To determine this conclusion, analytical relations are obtained for determining the poles of integrand expressions that fully describe surface, outflow and side waves. All the analytical results obtained correspond to Numerical calculations were carried out on some of the obtained ratios.Conclusion. The results showed that the power of the side waves is zero. It also follows from the calculations carried out that there is no radiation field of surface and outgoing waves, i.e. there is no contribution of them to the radiation pattern.

Miniaturized open-source 2LabsToGo screening of lactose-free dairy products and saccharide-containing foods

The open-source 2LabsToGo system is the only one in its nature. It combines in one miniaturized instrument all relevant steps normally performed in a chemical and biological laboratory. For the first time, the applicability of the 2LabsToGo system was studied for screening 17 food products. As examples, saccharides were analyzed in eight products of different matrix complexity, and the absence of lactose was studied in nine lactose-free dairy products. Derivatization including homogeneous reagent application and plate heating via the 2LabsToGo system was explored for saccharide detection, and its performance was investigated. The visual detection sensitivity of lactose was comparable to previous studies. The precision of lactose in milk matrix (%RSD 4.6%) as well as the coefficient of determination of the calibration function (0.9995) were highly satisfying. The obtained lactose content of milk (4.5%) was plausible. Screening eight saccharide-containing food samples showed the saccharides in agreement with the expectations for the respective food product. The lactose content of nine different lactose-free dairy products was proven to be below the 0.1% lactose limit value. As proof-of-principle and for verification, these screening results obtained with the miniaturized 2LabsToGo system were reproduced using conventional state-of-the-art instrumentation, which led to the same results. However, instrumental costs were comparably low for the 2LabsToGo system. The application of the new 2LabsToGo system was successfully shown for saccharide screening, which is attractive to the field of quality control or official food control.

Исследование разрушения и рационального распределения фазовых материалов в однородных и гибридных полиметаллических прямоугольных пластинах

Для прямоугольных полиметаллических пластин из изотропных материалов разработан общий метод нелинейно упругого и пластического их деформирования вплоть до разрушения. Метод основан на использовании классических кинематических гипотез Кирхгофа-Лява и соотношений физической связи напряжений и деформаций в фазовых материалах в форме деформационной теории пластичности с учетом влияния эффектов упрочнения. В качестве критерия разрушения использован критерий предельно допустимой деформации. Соответствующий переход от состояния упрочнения к состоянию разрушения. Считается, что несущая способность гибридной пластины реализуется если предельное состояние достигается одновременно во всех фазовых материалах. Рассматриваются произвольные условия закрепления контурных сторон прямоугольника (незакрепленные, защемленные, шарнирно-опертые) в любых комбинациях. Получены общие уравнения, подробно описан метод их решения при использовании современных модификаций метода Бубнова-Галеркина. Сформулирован критерий отбора рациональных проектов гибридных пластинок на основе совпадения нагрузок с эквивалентной по несущей способности однослойной пластинки. For rectangular polymetallic plates made of isotropic materials, a general method has been developed for their nonlinear elastic and plastic deformation up to failure. The method is based on the use of the classical Kirchhoff-Love kinematic hypotheses and the relationship between the physical connection of stresses and strains in phase materials in the form of a deformation theory of plasticity, taking into account the influence of hardening effects. The criterion of maximum allowable deformation is used as a failure criterion. Corresponding transition from the state of hardening to the state of failure. It is believed that the bearing capacity of a hybrid plate is realized if the limiting state is reached simultaneously in all phase materials. Arbitrary conditions for fixing the contour sides of a rectangle (loose, pinched, hinged) in any combination are considered. General equations are obtained, a method for their solution is described in detail using modern modifications of the Bubnov-Galerkin method. A criterion for selecting rational designs of hybrid plates based on the coincidence of loads with a single-layer plate equivalent in bearing capacity is formulated.

Three-dimensional scaled boundary finite element method to simulate Lamb wave health monitoring of homogeneous structures: Experiment and modelling

Exploiting scattering and reflection related data of ultrasonic Lamb wave interactions with damage is a common approach to health monitoring of thin-walled structures. Using thin PZT sensors, the method can be implemented in real-time. Simulation of Lamb wave propagation and its interaction with damage plays an important role in damage diagnosis and prognosis. It is, however, a time-consuming task due to the high-frequency waves that are commonly used to detect tiny damage. The current study employs the Scaled Boundary Finite Element Method (SBFEM) for effective modeling of Lamb wave health monitoring of homogenous thin plates. The electromechanical effects of piezoelectric sensors are included in the model to improve accuracy and make the results comparable to those of laboratory experiments. Simple meshing of complex topologies is possible by converting standard finite elements to scaled boundary elements. The 3D SBFEM wave motion equations are solved in the time domain to capture the sensor's PZT response to a high-frequency tone-burst actuation. The results are validated by pitch-catch and pulse-echo laboratory tests carried out on thin plates. SBFEM is used to study wave propagation in complex configurations, such as a stiffened plate, and the results are compared to their FEM counterparts. According to the findings, SBFEM significantly reduces the computational costs associated with simulation of Lamb wave health monitoring while also providing significant accuracy in comparison to the experimental results.

Free Vibration Analysis of a Functionally Graded Plate by Finite Element Method

A new category of materials (composite materials) is in full development, both in terms of their manufacture and calculation, in static and dynamic regime. These are Functionally Graded Materials used in the construction of various structural components such as beams and plates. In this paper, the authors present some results regarding the analysis of the free vibrations of a plane, circular plate, clamped on the boundary, made of such a material based on two constituent elements: alumina and aluminum. Two new, original concepts are introduced by the authors: the equivalent plate concept and the multilayer plate concept. The authors also present a study on the influence of the power coefficient of thr material laws on the natural frequencies of the plate. The the using of the multilayer plate concept is based on the replacement of the continuous variation (according to a given law) of the elastic properties with a step variation of them, according to the methodology proposed by the authors. The methodology of modal analysis proposed by the authors is validated by comparison with the results obtained analytically and numerically for homogeneous and isotropic plates. The results of the research undertaken by the authors are presented graphically and tabularly, representing the foundations of the formulated conclusions. These conclusions and especially the models and concepts presented in this paper are useful for the dynamic calculation of different types of structures made of functionally graded materials. The purpose of the work, that of presenting valid and easily accessible models and methodologies for the calculation of FGPs, is also fulfilled by using a widely spread and recognized software product (Ansys), using both common, simple finite elements and special finite elements (multilayer type), without any intervention in the respective stiffness matrices.

Reliability prediction of composite materials with random elastic inclusions

The object of the research is the construction of an algorithm that allows finding a number of strength (failure loading) statistical characteristics of a composite material plate under the conditions of a complex stress state. The relationships that determine the most probable value, mean value, dispersion and coefficient of variation of strength for an elastic homogeneous plate in which elliptical inclusions of another elastic material are uniformly distributed are written. Inclusions do not interact with each other and their geometric parameters are statistically independent random variables whose distribution laws are written for certain physical reasons.
 The combination of the known deterministic solution of the composite materials failure theory and probabilistic statistical methods that take into account the randomness of the material structure makes it possible to study the failure of composite materials taking into account the stochasticity of their structure.
 The main content of this article is the construction and analysis of the strength statistical characteristics algorithm of two-component lamellar composite materials. The mechanism of composite plate’s failure initiation in the inclusion is considered. The recorded relationships make it possible to calculate the most probable value, mean value, dispersion and coefficient of variation of strength and to investigate their dependence on the type of applied loading, structural heterogeneity of the composite and its dimensions (number of inclusions).
 The obtained results allow effective assessment of the reliability of stochastically defective two-component composite structural materials under complex stress conditions. This is due to the fact that the combined consideration of defectiveness and randomness in the composite material structure as interconnected, inseparable phenomena open new opportunities for researching of the strength problem and failure of composite materials under various types of applied loading.

Generalized thermoelastic waves in a homogeneous anisotropic plate with voids

AbstractIn this contribution, the thermoelastic Lamb waves in the homogeneous, transversely isotropic, plate with voids have been investigated in the context of classical and non‐classical theories of thermoelasticity. To investigate the problem, the fundamental governing equations have been developed in a unified way. On the solutions of these governing equations, the thermal and mechanical stress‐free boundary conditions, as well as constraints due to voids, have been imposed. The solutions of governing equations indicate that there exists a coupled system of wave motion called thermal waves (T‐mode), void wave motion (V‐mode), and elastic waves (E‐mode). However, the shear horizontal component of elastic wave decouples from the system is unaffected by elasto‐poro‐thermal coupling. For the symmetric and anti‐symmetric families of vibrations, the secular equation for the wave motion along with its special cases has been derived. To discover the wave characteristics, the secular equation has been solved using the numerical‐functional iteration method in MATLAB software, and the findings have been manifested by plotting the graphs. It has been concluded that the presence of voids affects the magnitudes of phase velocity, attenuation coefficient, and specific loss. This work may be helpful for geophysicists and engineers in the field of earthquake engineering. The developers of modern facilitating things such as acoustic touch screens, liquid viscosity sensors, etc. which are based on Lamb‐type wave propagation may also get benefitted.

Anti-impact performance of bionic tortoiseshell-like composites

Biological stiff-soft phase composite structures, such as tortoise shells and conch shells, have excellent anti-impact performance to withstand various types of high-stress events encountered in nature. A remarkable 3D interdigitating zigzag architecture in the tortoise shell, named occlusal suture structure, makes the tortoise shell simultaneously possess high mechanical strength and toughness, which is also an ideal stiff-soft phase composite prototype to mimic. In this study, four types of bionic anti-impact composite plates that feature the hard-soft phase architecture of tortoiseshell (Bio-T), mollusk shell (Bio-M), beetle exoskeleton (Bio-B) and nacre (Bio-N) and a homogeneous structure plate (HSP) are designed, to systematically examine and compare their roles in impact energy dissipation. Through an integrated approach combining additive manufacturing and drop tower testing, the peak force, residual velocity, and energy absorption of these bionic composite plates are studied and compared. Experimental results indicate that the Bio-T composite plate has the best impact resistance, compared with the other three bionic composites. Furthermore, the influence of the ply angle and the dimension of suture structure on the impact resistance of the Bio-T composite plate is identified. The [0°/30°/0°] arrangement is able to resist higher loads before failure. The 3D Bio-T composite plate provides a significant enhancement of anti-impact performance than the 2D Bio-T composite plate. Finally, the crack propagation mode in the suture structure of the Bio-T composite plates is examined, enhancing our understanding of the underlying mechanisms during impact. Such findings may prove useful for the design of future protective apparatus for soldiers and aircrafts, with improved anti-impact performance.

Study of Locking Compression Plate Through Biodegradable Implant

Orthopaedic implant biomechanics research is booming, especially in bone fixation. Fixation involves securing a plate to a broken bone. The femur fractured mostly. Long bone fractures can be difficult to cure despite technological and medical breakthroughs. This study analyses the performance and optimal screw arrangement for biodegradable locking compression plate. This study compares biodegradable bone plate materials to identify the best (Iron, Zinc and Magnesium). SolidWorks models fracture repair plates and fixes them in a normal walking condition to a mid-ship fracture. Further, finite element analysis was performed on models with homogeneous and isotropic bone and plate. Simulation was done using COMSOL programme and screws. Idealized poroelastic 3D FE femoral model with 5 mm fracture gap and plate-screw design. We saw stress and displacement. The minimal von Mises stress and deformation for 6 screws. Under pure zinc and magnesium load, the highest von Mises stress was 7.94 MPa and the maximum deformation was 0.08 mm, proving that iron was the best material. Based on finite element analysis, the LCP can offer mechanical stability for comminuted fractures, fixing the bone block and promoting bone healing.

Dislocation singularities in layered magneto-electro-elastic plates

A general and unified theory is formulated to investigate static and time-harmonic field solutions induced by dislocation loops and dislocation arrays in three-dimensional multilayered structures. Each homogeneous plate consists of an orthotropic magneto-electro-elastic material including nonlocal effects. While the nonlocal constitutive relations with multi-phase coupling are treated by means of the original Eringen model using a Helmholtz-type operator, the field expressions are based on the mathematically elegant and computationally powerful Stroh formalism in matrix form, consistently combined with double Fourier series expansions and the dual variable and position technique to propagate the extended solutions among the different layers of the multilayered systems. The time-harmonic dislocation loops are represented by a discontinuity in the prescribed elastic displacement, electric potential, and magnetic potential on arbitrarily-located rectangular and elliptical surfaces in the multilayered structures, while the dislocation arrays are composed of infinitely long, straight and uniformly spaced parallel dislocations with the same local Burgers vectors. The new field solutions are first validated against existing frameworks limited to static and local elasticity theory of these two types of extrinsic and intrinsic dislocations, and subsequently applied to analyze several unexplored effects on the dislocation-induced magneto-electro-elastic fields, namely the material anisotropy, interaction with internal heterophase interfaces, multi-phase coupling, nonlocal core-spreading parameter, finite-valued driving forces, vibration frequency, and stacking sequences. The numerical outcomes indicate that each effect is significant and neglecting any one of them leads to an erroneous prediction on the extrinsic and intrinsic dislocation-induced response, thus providing a suitable route for the design of advanced magneto-electro-elastic fabrication devices for energy harvesting applications.

Using the Equivalent Plate Concept to Calculate Functionally Graded Plates by Numerical Method

Functional graded materials are based on two materials, with very different properties, which vary continuously, according to a material law, on their thickness (a beam or a plate). The concept of equivalent plate involves the replacement of the given plate, a plate made of FGM, with a homogeneous and isotropic plate, with the same geometric characteristics (shape and dimensions), with the same load, which is attributed material properties that lead to the same behavior with the given plate. The aim of the paper is to provide a way to solve a complex problem (mathematical and structural), as in the case of FGM plates, with available means, with known professional calculation programs, with common finite elements, without intervention in the structure of its program. of finite element matrices, in other words without dedicated calculation programs. The finite element method is applied using the Ansys program and one of the best known finite elements, the 3D Solid185 element, both in the common version (structural) and in the multilayer finite element version.

Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor

Sandwich structures are widely used in construction, as well as in the aviation, spaceship, and electronics industries. The interesting result, among others, is the fact that individual layers can be freely selected to meet the planned requirements. In the case of sandwich structures in construction, they must meet the requirements of load-bearing capacity, thermal, and acoustic insulation, and additionally, they must be resistant to biological and chemical corrosion. The paper presents calculation algorithms for Hoff’s three-layer panels. In the first case, the well-known and proven method of finite differences in variation terms was used, assuming actual geometrical and material parameters. In the second case, the numerical homogenization method of the layered panel was used, replacing the stiffnesses of individual layers with a homogeneous equivalent plate with substitute stiffness corrected in shearing by an analytically derived shear correction factor. A comparative analysis of the results of the calculations with the use of both approaches was carried out. A good agreement between the displacement values and the calculated cross-sectional forces was obtained. On this basis, it can be assumed that the static analysis of a slab by simplified methods using numerical homogenization with an analytical shear correction factor is appropriate and can be applied to layer structures.

Analysis of the critical temperature on load bearing LSF walls under fire

Light Steel Frame (LSF) walls are widely used in building structures, used as partition walls and load bearing walls. The LSF is usually protected by layers of homogeneous plates or composite plates, with or without insulation materials in the cavity. This investigation presents the simulation results of composite LSF walls in reduced scale and full scale, based on variable load levels (20 to 80%). The numerical model uses a hybrid model approximation, based on the experimental tests to accurately determine the temperature field. The numerical model is validated with experimental results, at reduced and full scale, both at room temperature and under fire conditions. This modelling technique can follow the thermal and mechanical degradation of the protection layers of the LSF wall and determine the fire rating for load bearing (R) and insulation (I). The fire resistance (R) decreases with the increase of the load level. The insulation ability is also predicted for different protection materials. Relevant conclusions are presented to increase the insulation ability of LSF walls, especially when using non combustible double protection layers. The insulation ability to sustain fire usually increases with the number of studs and with the application of insulation material in the cavity region. The ability to sustain the load under fire also increases with the number of studs, especially for higher load levels. The ability to sustain the load also increases with the number of protection layers, changing from 16% at 20% load level, to 42% at 50% load level.A new proposal is presented for the critical temperature of the LSF, based on the maximum temperature of the LSF during the fire, allowing the calculation of the critical temperature, based on the load level of the specimen. This relation can predict the fire resistance time, based on the preliminary thermal analysis of the specimen. The reduced scale specimens present higher critical temperatures when compared to the full scale specimens, due to the typical failure mode (local modes for the reduced scale and global modes for the large scale).

Critical Temperature of Load Bearing LSF Walls Under Fire

AbstractLight Steel Frame (LSF) walls are widely used in building structures, used as partition walls and load bearing walls. The LSF is usually protected by layers of homogeneous plates or composite plates, with or without insulation materials in the cavity. This investigation presents the experimental and the simulation results of composite LSF walls in reduced scale and full scale, based on variable load levels (20 to 80%). The numerical model is validated with experimental results, at reduced and full scale, both at room temperature and under fire conditions. This modelling technique can follow the thermal and mechanical degradation of the protection layers of the LSF wall and determine the fire rating for load (R) and insulation (I). The fire resistance (R) decreases with the increase of the load level, being the critical temperature of the steel structure presented by the maximum temperature of the Hot Flange (HF). A new proposal is presented for the critical temperature of the LSF, based on the maximum temperature of the LSF during the fire. The insulation ability is also predicted for different protection materials. Relevant conclusions are presented to increase the insulation ability of LSF walls.

Vibration Response Analysis of Tapered Porous FGM Plate Resting on Elastic Foundation

This paper attempts to demonstrate the vibration response of porous Functionally Graded Material (FGM) plate with variable thickness. For the first time, the porous tapered FGM plate being considered is mathematically modeled and assumed to be resting on a linear, parabolic, sinusoidal, and exponential varying Winkler’s elastic foundation. The even and uneven porosity distribution as a micro-defect is assumed in a tapered FGM plate that varies according to well-defined mathematical rules. The tapered FGM plate, across the edges, is supported with various boundary conditions. Simple Power (P-) and Sigmoid (S-) Law have been chosen for the homogenization of material properties that are tailored in the thickness direction. First-order shear deformation theory (FSDT) is applied to describe the displacement function for computing the strain field. The variational approach has been used to establish the formulation for free vibration response. The equation of motion has been derived using Hamilton’s principle and solved by implementing Galerkin Vlasov’s method. Parametric studies on elastic foundations have been done to explore the results and relevance to the real problems. It was observed that variable foundation has a significant effect on the tapered FGM plate rather than the tapered homogenous plate. In addition, it was witnessed that the effect of variable foundation effect diminishes as a constraint on the edges of the tapered FGM plate increases. Also, some benchmark results based on the porosity effect and the influence of variable elastic foundations are exhibited in this study for future reference.

Mimicking biological architectures via freeze casting

Mimicking biological materials with sophisticated hierarchical structures composed of low-dimensional building blocks has attracted significant attention. Particularly, developing efficient, scalable preparation approaches for structural and functional biomimetic architectures to advance the understanding of structure-property relationships is of vital importance yet remains highly challenging. This preview discusses a recent contribution from H. Bai and co-workers who developed a facile combination of bidirectional freeze casting, water-vapor annealing, and densification treatment to construct sustainable nacre-mimetic silk-based composites with a typical "brick-and-mortar" structure. The biomimetic design of the single component "Silk nacre" renders the material's mechanical properties superior to those of homogeneous solvent-casted silk plates and many frequently employed polymers. Moreover, the Silk nacre was able to be manufactured into various shapes with excellent mechanical stability as well as be completely biodegraded, which showed the durable and environmentally friendly biomimetic architectures as next-generation structural and functional materials.

An equivalent modelling approach for vibroacoustic characteristics analysis of railway aluminium extrusion

For railway carbody structures with irregular cross-sectional shapes and great longitudinal lengths, it is difficult to obtain their vibroacoustic characteristics using traditional computational methods. Moreover, traditional methods are time intensive and not conducive to the optimisation design of such complex and large structures. This study introduces an equivalent modelling approach for vibroacoustic analysis, i.e., sound transmission loss and sound radiation analysis, of railway aluminium extrusion. The aluminium extrusion is equivalent to a homogeneous orthotropic plate, and the equivalent mechanical properties of the plate are obtained via static analysis based on the small-deflection theory. The vibroacoustic characteristics are obtained using the hybrid method of finite element and statistical energy analysis. First, the equivalent modelling approach is validated using the results of a detailed prediction model and experimental test. Subsequently, the applicability of the equivalent approach is analysed by comparing it to the predicted results of the detailed model with different dimensions and boundary conditions. Ultimately, the minimum longitudinal length that needs to be considered for the analysis of railway aluminium extrusion is discussed using the equivalent approach and the computational efficiency is compared. The results reveal that the equivalent approach can effectively simulate the vibroacoustic performances of the aluminium extrusion in 1/3 octave bands centred below 1000 Hz and reduce the calculation time by 90% compared with the detailed prediction models of aluminium extrusion, which provided a foundation for vibroacoustic optimisation design of railway carbody structures.

A three‐phase laminated anisotropic elliptical inhomogeneity with internal uniform stress resultants

AbstractWe use the Stroh octet formalism for the coupled stretching and bending deformations of Kirchhoff laminated anisotropic thin plates together with the complex variable formulations of the decoupled stretching and bending deformations of Kirchhoff homogeneous isotropic thin plates to study the internal stress resultants inside a laminated anisotropic elliptical inhomogeneity bonded to a surrounding infinite laminated anisotropic matrix through a confocal interphase layer composed of a homogeneous isotropic plate when the matrix is subjected to uniform remote membrane stress resultants and bending moments. We prove that for given geometric and material parameters of the composite, the internal stress resultants inside the elliptical inhomogeneity are uniform when four specific conditions on the remote loading are satisfied. Furthermore, the internal uniform elastic field is determined in real‐form in terms of the two 8 × 8 fundamental elastic plate matrices for both the inhomogeneity and the matrix and the three 4 × 4 real matrices S, H, and L for the matrix.