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Transient thermoelastic interactions between materials and the moving heat sources, i.e. Laser additive manufacturing, Laser-assisted thermotherapy, high speed sliding and rolling contacts, are becoming increasingly important. In this work, a unified fractional thermoelastic theory is developed, and applied to study transient responses caused by a moving heat source. Theoretically, new insights on fractional thermoelasticity are provided by introducing new definitions of fractional derivative, i.e. Caputo-Fabrizio, Atangana–Baleanu and Tempered-Caputo type. Numerically, a semi-infinite medium subjected to a source of heat moving with constant velocity is considered within the present model under two different sets of boundary conditions: stress free and temperature given for the first, displacement fixed and thermally adiabatic for the second. Analytical solutions to all responses are firstly formulated in Laplace domain, and then transformed into time domain through numerical method. The numerical results show that Caputo-Fabrizio and Atangana–Baleanu type models predict smaller transient responses than Caputo type theory, while Tempered-Caputo model may give larger results by increasing the tempered parameter. Meanwhile, the effect of fractional order, tempered parameter of Tempered-Caputo model, and the velocity of heat source on all responses is discussed in detail. The time history of responses shows that: for long-term process, the exponential function of TC definition will make sense, and the temperature from TC model is greatly different from that of C model. This work may provide comprehensive understanding for thermoelastic interactions due to moving heat source, and open up possibly wide applications of such new fractional derivatives.

Dielectric elastomers (DEs) are a category of soft electro-active materials that can be used as sensors, actuators and generators. In order to provide protection, insulation layers are essential and thicker layers can lead to stronger protecion. However, the presence of the additional layers can certainly constrain the deformation of DEs. Thus a balance between protection and performance is needed. Prestretch is widely used for the enhancement of actuation performance. Thus the DE membrane integrated with protective passive layers is studied here, focusing on the effect of the coexistence of the prestretch and passive layers. We identify two approaches of prestretches, where the DE membrane and protective passive layers can be explicitly prestretched by external loads, or the DE membrane can be implicitly prestretched by solely protective passive layers. For the latter approach, it does not require additional components such as rigid clamps or dead weights. We then establish a coupled model for the DE membrane and passive layers. The effects of the prestretches and passive layers on the electromechanical behavior and voltage-induced deformation of the DE membrane are then revealed numerically. Furthermore, we theoretically study the detailed effects of specific mechanical properties of passive layers such as the thickness and shear modulus, which are useful for the design of the system. This theoretical research thus sheds insights for the design of dielectric elastomer applications where both safety and performance are required.

New insights on theoretical modeling of size-dependent functionally graded (FG) nanobeams are provided by establishing a unified theory of 2n+1 order shear deformable model with the aids of nonlocal strain gradient elasticity. The unified model covers Euler-type (n = 0), Reddy-type (n = 1), 5th (n = 2), 7th (n = 3) order beam and etc., and the limiting situation n → ∞ predicts nonlocal strain gradient Timoshenko model. The mathematical difficulty for FG nonlocal parameter is particularly emphasized, and an attempt is made for the first time to overcome the difficulty. Theoretically, the governing equations and boundary conditions of 2n+1 order nonlocal strain gradient beams, especially with FG nonlocal parameter and FG strain gradient parameter, are systematically formulated. The difficulty for FG nonlocal parameter is satisfactorily solved with by adopting the present 2n+1 order beam theory. Analytically, solutions to bending and buckling analyses within the unified model are obtained, from which the analytical solutions for Euler- and Timoshenko-type beam can be recovered. Numerically, bending deflection and buckling critical load for Euler beam, Reddy beam, 5th-11th order beam and Timoshenko beam are depicted, of which the benchmark solutions for the 5th to 11th order beam are given for the first time. Meanwhile, potential extensions of the unified model into fractional order is discussed, where benchmark solutions for n = 1.1, 0.88, 0.77, 0.4and0.2 are listed. The influences of FG nonlocal parameter, dimensionless height and Poisson's ratio (or the ratio E/G) on the bending deflection and buckling critical load are systematically studied. The present work mainly contributes to theoretical developments and greatly facilitates the mechanical analysis of beam-type structures.

This work develops a regularized least absolute deviation-based sparse identification of dynamics (RLAD-SID) method to address outlier problems in the classical metric-based loss function and the sparsity constraint framework. Our method uses absolute derivation loss as a substitute of Euclidean loss. Moreover, a corresponding computationally efficient optimization algorithm is derived on the basis of the alternating direction method of multipliers due to the non-smoothness of both the new proposed loss function and the regularization term. Numerical experiments are performed to evaluate the effectiveness of RLAD-SID using several exemplary nonlinear dynamical systems, such as the van der Pol equation, the Lorenz system, and the 1D discrete logistic map. Furthermore, detailed numerical comparisons are provided with other existing methods in metric-based sparse regression. Numerical results demonstrate that (1) RLAD-SID shows significant robustness toward a large outlier and (2) RLAD-SID can be seen as a particular metric-based sparse regression strategy that exhibits the effectiveness of the metric-based sparse regression framework for solving outlier problems in a dynamical system identification.

In this work, a three characteristic-lengths featured size-dependent gradient-beam is constructed by adopting the modified nonlocal model, resulting in much more general constitutive equation with stress gradient up to four-order and strain gradient to two-order. The six-order differential governing equation for transverse displacement is formulated. All boundary conditions especially variational consistent higher order boundary conditions of the present model are derived with the aid of weighted residual approach. The closed-form solutions to critical buckling loads under different sets of boundary conditions are systematically formulated with higher order boundary conditions incorporated. The numerical results show that both nonlocal parameters have significant effect on the buckling behaviors. Meanwhile, if two nonlocal parameters are taken as same, the present results cannot always reduce to that from Eringen's nonlocal model. Due to its clear physical meaning, the present model is expected to be widely adopted in mechanical analyses of nano-structures.

To adapt to various environments, many intelligent robots have incorporated components of variable stiffness, which typically vary transiently. In order to design appropriate forms of stiffness variation, it is important to study how such variations can affect the system’s dynamic behaviors. This study investigates a hub–beam system with transient variable stiffness under large-scale motion. We consider two forms of transient variable stiffness: a step-like variation and periodic variations. Although the step-like variation is simple, it can induce complex response dynamics, and hence, it is difficult to predict the vibration amplitude. This difficulty, however, can be avoided by considering transient periodic variable stiffness. For this type of variation, resonance-like behaviors are observed, where the amplitude initially increases exponentially with time and becomes stationary after the stiffness stops varying. Such transient nature of stiffness variation can significantly affect resonance behaviors, including resonance amplitudes and the number of resonance regions. Based on these findings, we present a method to design optimal periodic variable stiffness for reducing vibrations. Our results provide insights into the design, utilization, and control of transient variable stiffness systems, particularly for many robots with variable components, where reducing vibrations is important.

This paper studies a variable length elastica with a fixed point constraint by an assembly method that regards the whole elastica as an assembly of two components, i.e., pinned-clamped elasticas. The pinned-clamped elastica is obtained based on the post-buckled deformed shape with one internal inflection point. Thus, multiple coexisting solutions can be located accurately, which reveals three distinct equilibrium paths for the complete load–displacement curves. Under displacement control, two critical points on two equilibrium paths are found at saddle-node bifurcations. Interestingly, a new critical point is located at the boundary point of one equilibrium path, where the shapes of two pinned-clamped elasticas are two different post-buckled deformed shapes. Changing the location of the fixed point constraint allows the position of the boundary point to be easily manipulated, and the associated snap-through phenomenon can occur on different equilibrium paths. This flexible generation of the snap-through phenomenon is useful for designing engineering systems that require controllable snap-through.

This work is aimed at establishing a unified fractional thermoelastic model for piezoelectric structures, and shedding light on the influence of different definitions on the transient responses. Theoretically, based upon Cattaneo-type equation, a unified form of fractional heat conduction law is proposed by adopting Caputo Fabrizio fractional derivative, Atangana Baleanu fractional derivative and Tempered Caputo fractional derivative. Then, thermoelastic model of fractional order is formulated for piezoelastic materials by combining the unified heat conduction law and the governing equations of elastic and electric fields. Numerically, the present theoretical model is applied to study the transient responses of piezoelectric medium that is subjected to a thermal shock. The governing equations are analytically derived and numerically solved with the aids of Laplace transform method. The obtained results are graphically illustrated, and the influences of different definitions of fractional derivative and different fractional order are revealed. This work may be helpful for understanding the multi-coupling effect of elastic, thermal and electric fields, and for inspiring further developments of fractional calculus.

This work is devoted to investigate the flow behavior and microstructure evolution of AlSi10Mg by additive manufacturing in hot deformation. Tensile test is carried out under different temperatures, i.e. 200 ∘ C, 250 ∘ C, 300 ∘ C, 350 ∘ C and 400 ∘ C, with various strain rates of 0.004/s, 0.002/s and 0.0004/s. Theoretically, the modified Arrhenius-type model of additive manufacturing materials at high temperature is established. Experimentally, scanning electron microscope and optical microscope are used to analyze the mechanism of hot deformation. It is found that at 200 ∘ C both the dendritic eutectic Si and acicular eutectic Si precipitate, forming cellular structure and strengthening phases. And then, the acicular eutectic Si is partially dissolved into Al matrix, but there is no obvious growth of dendritic Si at 300 ∘ C. With the temperature increasing, the cellular structure and melt pool boundary gradually disappear. For 400 ∘ C temperature, like homogenization process, the precipitation of saturated solid solution forms the dispersed phase, and the stress-strain curve shows a weak hardening. Meanwhile, the statistical result shows that that the constitutive model agrees well with the experimental results at high temperature. This study may provide guidance for the improvement of additive manufacturing material properties by post-treatment.

This paper studies the snap-through of a pinned-clamped elastica when the support of the clamped end can be moved arbitrarily in plane. The universal snap curve, which describes the critical boundary conditions of the pinned-clamped elasticas, is firstly obtained by determining the saddle-node bifurcation points of the moment-rotation response curves. Based on the universal snap curve, the stability of the pinned-clamped elastica can be determined when the support at the clamped end is moved. The critical boundary can also be directly obtained, where the elastica loses stability and the snap-through occurs between the non-inverted shape and the inverted shape. This study can be useful to reveal the snap-through behavior for some other complex systems where movable supports exist.

Sintering of layered metal fiber sheets produces a structured, tunable, paper-like material that holds promise for thermal and biomaterial applications. Particularly promising for these areas is a material system synthesized by the sequential-overlap method, which produces a networked, transversely isotropic open cell porous material. Engineering application of these materials has been limited due in part to uncertainty about their mechanical responses. Here, we present a comprehensive structural and mechanical characterization of these materials, and define a modeling framework suitable for engineering design. X-ray tomography revealed a layered structure with an isotropic fiber distribution within each layer. In-plane uniaxial compression and tension tests revealed a linear dependence of Young's modulus and yield strength upon relative fiber density. Out-of-plane tests, however, revealed much lower Young's modulus and strength, with quartic and cubic dependence upon relative density, respectively. Fiber fracture was the dominant mode of failure for tension within the “in-plane” directions of the fiber layers, and fiber decohesion was the dominant mode of failure for tension applied in the “out-of-plane” direction, normal to the layers. Models based upon dispersions of beams predicted both in-plane and out-of-plane elastoplastic properties as a function of the relative density of fibers. These models provide a foundation for mechanical design with and optimization of these materials for a broad range of potential applications.

This work is devoted to study the mechanical behaviors of polylactic acid (PLA) materials from additive manufacturing, and an orthotropic model is established to predict the mechanical properties under arbitrary printing orientation. Firstly, the morphology of PLA material is analyzed by using scanning electron microscopy, from which the orthotropic behavior of PLA material is obtained. Three printing planes are adopted, and on each printing plane different printing angles may be selected. The mechanical parameters, including Young's modulus, yielding stress, and Poisson's ratio, for material under different printing directions are determined via quasi-static experiments. Secondly, the orthotropic constitutive model of PLA materials under different printing angles is thus obtained, and the prediction method of orthotropic mechanical properties is built based on the coordinate transformation matrix, where the orthotropic coordinate transformation matrix is acquired by attitude angles (i.e., Euler angle, the rotation angle of the local coordinate system relative to the global coordinate system). Finally, the theoretical prediction method was verified, and high-quality printing methods were recommended. In addition, the obtained results of the model show that: for PLA material, the orthotropic hypothesis model is superior to the transverse isotropic hypothesis one. This present method is not only suitable for predicting the constitutive model of printed specimens in any direction but also for other materials of fused deposition modeling.

Microscale transient thermoelastic responses are becoming significantly important with the rapid developments and wide applications of MEMS/NEMS. However, thermal transport and elastic deformation at such scale can't be well described by classical Fourier's law and elastic theory. In this work, theoretical derivation of gradient-type thermoelasticity with electron-lattice coupling mechanism for micro scale metals is systematically given with the aids of generalized thermodynamics and electron-lattice heat conductive model. Numerically, the present model is applied to study the microscale thermoelastic behaviors of a slim strip subjected to thermal shock. For such transient issue, Laplace transform method is adopted, and the analytical solutions are firstly obtained in the Laplace domain, then transient thermoelastic responses for time domain are gotten by numerical inverse Laplace transform method. The results demonstrate that the present model predicts larger responses than that from classical thermoelasticity, such as: higher temperature, larger stress, and bigger heat affected region. Meanwhile, parametric studies are conducted to evaluate the influence of stress gradient parameter, heat flux gradient parameter, and relaxation times on the transient responses, from which a simplified version of microscale thermoelasticity is finally recommended.

A thick-walled cylinder under outer pressure load was studied by means of the Finite cell method (FCM). Sensitivity analysis was made to demonstrate the advantage of this method. Shape optimization of a turbine disk is conducted. It is shown that the introduction of B-spline basis function can achieve a high continuity of stress filed along the cell boundary.

PurposeThe purpose of this paper is to study the buckling and the vibration of the beam induced by atom/molecule adsorption using the nonlocal Euler‐Bernoulli beam model with initial axial stress.Design/methodology/approachThe nonlocal parameter associated with adsorbed mass and bending rigidity variations of the beam induced by adsorbates are taken into account, and the buckling and dynamic behaviors are obtained via the Hamilton's principle, in which the potential energy between adsorbates and surfaces of the beam, the bending energy, the external work and the kinetic energy are summed as the Lagrangian function.FindingsThe results show that, for both buckling and resonant frequency, the nonlocal effect should be considered when the beam scales down to several hundreds of nanometres, especially for higher mode numbers.Originality/valueThe present paper gives the exact expressions for the buckling and resonant frequency of a simple‐supported nonlocal beam with initial axial stress. Different from previous works, the mass increasing and bending rigidity of the beam are found size‐dependent (nonlocal effect), resulting in possible different static and dynamic behaviors of the beam when atom/molecular adsorption occurs. The exact expressions obtained for the buckling and resonant frequency may be helpful to the design and application of micro‐ and nanobeam‐based sensors/resonators.

In the present paper, a general solution involving three arbitrary functions for the generalized (2+1)-dimensional KdV-mKdV equation, which is derived from the generalized (1+1)-dimensional KdV-mKdV equation, is first introduced by means of the Wiess, Tabor, Carnevale (WTC) truncation method. And then multisymplectic formulations with several conservation laws taken into account are presented for the generalized (2+1)-dimensional KdV-mKdV equation based on the multisymplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from the general solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent to the Preissmann scheme. From the results of the numerical experiments, we can conclude that the multi-symplectic schemes can accurately simulate the periodic wave solutions of the generalized (2+1)-dimensional KdV-mKdV equation while preserve approximately the conservation laws.

A bolt-ball is a commonly joint form in latticed shells. It’s a typical semi-rigid joint, which can bear certain amount of bending moment. The performance of triangle mesh single-layer cylinder shells with bolt-ball joints in different support conditions has been analyzed detailed using the finite element (FE) software ANSYS based on several different parameters including bending stiffness, torsional stiffness, shell span, ratio of rise to span, ratio of length to width and load distribution in this paper, and key influence parameters to the load carrying capacity of cylinder shells with semi-rigid joints in different support conditions are obtained. Finally, based on the results obtained by FE calculation, a new formula is proposed for getting ultimate load of single cylinder shells with semi-rigid joints in four sides support, some references are provided for shell design.

Based on the generalized Hamiltonian principle and the first-order approximation coupling (FOAC) model theory, a fully coupled nonlinear model for a rotating flexible smart structure with a tip mass is proposed, in which the geometrically nonlinear effects of the piezoelectric layers coupled with the structure and the structural large deformation are considered. Then the vibration control of the above system is discussed by the slide mode control (SMC) method. In the process of control design, the optimization approach and Lyapunov stability theory are used to determine the sliding surface of SMC and the control signal, respectively. The simulation results show that SMC approach is effective for the vibration suppression of the rotating flexible smart structure with parameter perturbation uncertainties and large deformation.

A discrete sliding mode control (SMC) method based on hybrid model of neural network and nominal model is proposed to reduce the vibration of flexible structures, which is a robust active controller developed by using a sliding manifold approach. Since the thick boundary layer will reduce the virtue of SMC, the multilayer feed-forward neural network is adopted to model the uncertainty part. The neural network is trained by Levenberg-Marquardt backpropagation. The design objective of the sliding mode surface is based on the quadratic optimal cost function. In course of running, the input signal of SMC come from the hybrid model of the nominal model and the neural network. The simulation shows that the proposed control scheme is very effective for large uncertainty systems.

This paper presents an improved symplectic precise integration method (PIM) to increase the accuracy and keep the stability of the computation of the rotating rigid–flexible coupled system. Firstly, the generalized Hamilton's principle is used to establish a coupled model for the rotating system, which is discretized and transferred into Hamiltonian systems subsequently. Secondly, a suitable symplectic geometric algorithm is proposed to keep the computational stability of the rotating rigid–flexible coupled system. Thirdly, the idea of PIM is introduced into the symplectic geometric algorithm to establish a symplectic PIM, which combines the advantages of the accuracy of the PIM and the stability of the symplectic geometric algorithm. In some sense, the results obtained by this method are analytical solutions in computer for a long span of time, so the time-step can be enlarged to speed up the computation. Finally, three numerical examples show the stability of computation, the accuracy of solving stiff equations and the capability of solving nonlinear equations, respectively. All these examples prove the symplectic PIM is a promising method for the rotating rigid–flexible coupled systems.

The Riccati-Bernoulli sub-ODE method is firstly proposed to construct exact traveling wave solutions, solitary wave solutions, and peaked wave solutions for nonlinear partial differential equations. A Backlund transformation of the Riccati-Bernoulli equation is given. By using a traveling wave transformation and the Riccati-Bernoulli equation, nonlinear partial differential equations can be converted into a set of algebraic equations. Exact solutions of nonlinear partial differential equations can be obtained by solving a set of algebraic equations. By applying the Riccati-Bernoulli sub-ODE method to the Eckhaus equation, the nonlinear fractional Klein-Gordon equation, the generalized Ostrovsky equation, and the generalized Zakharov-Kuznetsov-Burgers equation, traveling solutions, solitary wave solutions, and peaked wave solutions are obtained directly. Applying a Backlund transformation of the Riccati-Bernoulli equation, an infinite sequence of solutions of the above equations is obtained. The proposed method provides a powerful and simple mathematical tool for solving some nonlinear partial differential equations in mathematical physics.

In the present paper, the computation for the nonlinear dynamic system is discussed. Firstly the nonlinear dynamic system is converted into an augmented dynamic system in the Minkowski space, which results in the system of Lie type locally. Then Runge–Kutta Munthe-Kaas (RKMK) methods are used to the new augmented dynamic system and group-preserving integration scheme for the augmented dynamic system is constructed, in which the precise integration method is used to compute the exponential mapping. In the process of computation, the numerical schemes are formulated for nonlinear dynamic system directly. The advantages of the method presented in this paper lie in not only its group-preserving character but also in its simplicity.

In the present paper, based on the classical Magnus expansion, a simple and efficient fourth-order integrator is given for an arbitrary nonlinear dynamic system, which can preserve the qualitative properties of the exact solution. The proposed method can be considered an averaging technique, and only requires evaluations of exponentials of simple unidimensional integrals. Finally, the numerical examples are given to demonstrate the validity and effectiveness of the method of this paper.

Beam-type periodic materials with high connectivity have displayed unique band gap behaviors analogous to locally resonant band gaps in acoustic metamaterials. In this study, structurally square re-entrant honeycomb, one highly connected lattice configuration featuring eight folded beams connected at each joint, is introduced to be the host structure of a smart material to tailor the elastic wave propagation. Finite length piezoelectric patches connected with negative capacitance shunting circuits are arranged on the beam surfaces, providing active adjustment via altering the parameters of shunting circuits. The characteristics of band structure of this smart structured material are investigated through the application of finite element method in conjunction with the Bloch theorem. Results demonstrate that the variation of internally resonant band gaps induced by the alteration of the piezoelectric patches to those positions and mechanical properties, can be precisely estimated by simple heuristic models proposed according to deformation characteristics of standing wave modes. This founding could promote the practical implementation of the highly connected honeycombs in the adaptive control to elastic wave.

Switching dynamics among saddles in a network of nonlinear oscillators can be exploited for information encoding and processing (hence computing), but stable attractors in the system can terminate the switching behavior. An effective control strategy is presented to sustain switching dynamics in networks of pulse-coupled oscillators. The support for the switching behavior is a set of saddles, or unstable invariant sets in the phase space. We thus identify saddles with a common property, localize the system in the vicinity of them, and then guide the system from one metastable state to another to generate desired switching dynamics. We demonstrate that the control method successfully generates persistent switching trajectories and prevents the system from entering stable attractors. In addition, there exists correspondence between the network structure and the switching dynamics, providing fundamental insights on the development of a computing paradigm based on the switching dynamics.

Focusing on the local conservation properties, a nine-point implicit difference scheme derived from the multi-symplectic idea, which is named as a generalized multi-symplectic integrator, is presented for the Burgers equation firstly. And then, the associated proofs needed on the local conservation properties of the scheme are given in detail. Finally, to illustrate the high accuracy, the good local conservation properties as well as the excellent long-time numerical behavior of the scheme, the numerical experiments on the single-front solution of the Burgers equation by the implicit scheme are reported.