We investigate different variants of the method of fundamental solutions for solving scattering problems from infinite elastic thin plates. These provide novelty and desirable ease of implementation ...as direct accurate and fast solvers to be used iteratively in solving the corresponding inverse problems. Various direct problems associated with physical states of clamped, simply supported, roller–supported and free plates can be solved efficiently using the proposed meshless method. In particular, the numerical implementation performed for clamped plates leads to results showing very good agreement with the analytical solution, where available, and with previously obtained boundary integral method solutions. As for the inverse obstacle identification, the study further develops a constrained nonlinear regularization method for identifying a cavity concealed in an infinite elastic thin plate that has important benefits to the structural monitoring of aircraft components using non–destructing material testing.
•Numerical solution of scattering problems from infinite elastic thin plates with the method of fundamental solutions.•Four variants of the method of fundamental solutions are proposed.•Excellent agreement with existing results obtained with other numerical methods is reported.•Investigation of the corresponding inverse geometric problem.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this Letter, we report on the design and experimental characterization of a broadband acoustic hyperbolic metamaterial. The proposed metamaterial consists of multiple arrays of clamped thin plates ...facing the y direction and is shown to yield opposite signs of effective density in the x and y directions below a certain cutoff frequency, therefore, yielding a hyperbolic dispersion. Partial focusing and subwavelength imaging are experimentally demonstrated at frequencies between 1.0 and 2.5 kHz. The proposed metamaterial could open up new possibilities for acoustic wave manipulation and may find usage in medical imaging and nondestructive testing.
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CMK, CTK, FMFMET, IJS, NUK, PNG, UM
This paper presents an isogeometric analysis (IGA) based design method to address the stress-constrained topology optimization problem of plane stress and bending of thin plates. Based on the popular ...SIMP model, the integrated framework of geometry modeling, structural stress analysis and optimization is established. Owing to the geometry exactness and high-order continuity between elements, the IGA improves the computational accuracy of stress, and thus enhances the credibility of optimum design. Meanwhile, the obvious zigzag boundaries are avoided in the optimized results, and the stress function of IGA maintains the continuity for a relatively coarse discretization. Moreover, the IGA-SIMP method can easily meet the requirement of C1-continuity for the Kirchhoff plate formulations, which also facilitates the stress analysis and sensitivity calculation. To overcome the convergence difficulty of highly nonlinear stress aggregation constraint, two STM (stability transformation method)-based stabilization schemes combining with the P-norm function for global stress constraint are developed to achieve the stable iterations and acceptable designs. Finally, representative examples illustrate the effectiveness and convenience of the proposed approach. It is indicated that the IGA-SIMP method shows superior performance for solution accuracy and efficiency, and the local stress level is well controlled.
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•A mathematical model is proposed to describe the nonlinear damping phenomenon of FRCTP in an amplitude-dependent manner.•The elastic moduli are expressed as the function of strain energy ...density.•The loss factors in different fiber directions are expressed as the functions of the excitation amplitude.•The amplitude dependent coefficients of fiber-reinforced composite are determined by quintic polynomial fitting method.•TC300 carbon/epoxy composite plates are used to verify the correctness of the theoretical model.
A damping model of fiber reinforced composite thin plate with consideration of amplitude-dependent property is established using the Jones–Nelson nonlinear theory in conjunction with the classical laminated plate theory, polynomial fitting method and strain energy method. In this model, the elastic moduli are expressed as the function of strain energy density and the loss factors in the longitudinal, transverse and shear directions are expressed as the functions of excitation amplitude. Moreover, three TC300 carbon/epoxy composite plates are taken as research objects to carry out a case study. One of them is used to determine the amplitude-dependent coefficients of loss factors in fiber reinforced composites by combining the least square method with polynomial fitting method, and the other two plates are used to verify the correctness of the theoretical model. The results of the developed model considering amplitude dependence and experimental test show a good consistency. It is discovered that the viscoelastic effect of epoxy resin materials will contribute to the increased degree of damping. So, if such plate structures exhibit more pronounced viscoelastic characteristics, there will be more significant in the nonlinear degree of amplitude-dependent damping phenomenon.
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•Laminated Kirchho nanoplates are analyzed considering the strain gradient theory.•A finite element method is developed to evaluate frequencies and buckling loads.•Higher-order requirements in terms ...of element continuity are enforced.•Membrane and bending degrees of freedom are approximated through Hermite functions.•A wide validation procedure based on analytical methods is presented.
The paper presents a finite element method to investigate the critical buckling loads and the natural frequencies of laminated Kirchhoff plates including the nonlocal strain gradient effect, which could have considerably consequences at the nanoscale. With respect to the existing literature, the proposed numerical methodology is developed to deal with general stacking sequences of orthotropic layers with arbitrary orientations and various boundary conditions. The resulting membrane-bending coupling is emphasized in the formulation, which requires to study the whole set of partial differential equations. The membrane and bending degrees of freedom are all approximated by means of Hermite interpolating functions with higher-order continuity requirements. To this aim, regular rectangular finite elements based on conforming (C) and nonconforming (NC) approaches are used. A wide validation procedure is carried out to prove the effectiveness of the proposed formulation. A set of new results is presented for general mechanical configurations with arbitrary restraints.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
This paper adopts a modified Fourier-Ritz approach to study the free vibration characteristics of orthotropic circular, annular and sector thin plates subjected to general boundary conditions. For ...the arbitrary plate forms and the boundary conditions, the displacements can be written in the form of a standard Fourier cosine series supplemented with several auxiliary functions. The auxiliary functions, which are closed-form and introduced to remove all the potential discontinuities of the original displacement function and its derivatives in the whole domain, can be usefully employed in improving the convergence of the results. The artificial boundary spring technique and artificial coupling spring technique are adopted to simulate the arbitrary boundary conditions and to ensure appropriate continuity conditions along the radial edges, respectively. Because the displacement field is sufficiently smooth in the whole solution domain, the accurate solution can be obtained by using the Ritz procedure on the basis of the energy functions. The accuracy, reliability and versatility of the current method are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions.
Crystal lattices with tetragonal or hexagonal structure often exhibit structural transitions in response to external stimuli
. Similar behaviour is anticipated for the lattice forms of topological ...spin textures, such as lattices composed of merons and antimerons or skyrmions and antiskyrmions (types of vortex related to the distribution of electron spins in a magnetic field), but has yet to be verified experimentally
. Here we report real-space observations of spin textures in a thin plate of the chiral-lattice magnet Co
Zn
Mn
, which exhibits in-plane magnetic anisotropy. The observations demonstrate the emergence of a two-dimensional square lattice of merons and antimerons from a helical state, and its transformation into a hexagonal lattice of skyrmions in the presence of a magnetic field at room temperature. Sequential observations with decreasing temperature reveal that the topologically protected skyrmions remain robust to changes in temperature, whereas the square lattice of merons and antimerons relaxes to non-topological in-plane spin helices, highlighting the different topological stabilities of merons, antimerons and skyrmions. Our results demonstrate the rich variety of topological spin textures and their lattice forms, and should stimulate further investigation of emergent electromagnetic properties.
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