Wrinkling in graded core/shell systems using symplectic formulation

Wrinkles in flat graded elastic layers have been recently described as a timevarying Hamiltonian system by the energy method.Cylindrical core/shell structures can also undergo surface instabilities under the external pressure.In this study,we show that by treating the radial direction as a pseudo-time variable,the graded core/shell system with radially decaying elastic properties can also be described within the symplectic framework.In combination with the shell buckling equation,the present paper addresses the surface wrinkling of graded core/shell structures subjected to the uniform external pressure by solving a series of ordinary differential equations with varying coefficients.Three representative gradient distributions are showcased,and the predicted critical pressure and critical wave number are verified by finite element simulations.The symplectic framework provides an efficient and accurate approach to understand the surface instability and morphological evolution in curved biological tissues and engineered structures.

Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method（FEM） results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli（EB） beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.

A procedure of the method of reverberation ray matrix for the buckling analysis of a thin multi-span plate

A procedure of the method of reverberation ray matrix(MRRM)is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners.A computation algorithm for the reverberation ray matrix in the MRRM is derived to determine the buckling loading.Specifically,the analytical solutions are presented for the buckling of the structure having two opposite simply-supported or clamped-supported edges with spans,while the constraint condition of two remaining edges may be in any combination of free,simply-supported,and clamped boundary conditions.Furthermore,based on the analysis of matrices relating to the unknown coefficients in the solution form for the deflection in terms of buckling modal functions,some recursive equations(REs)for the MRRM are introduced to generate a reduced reverberation ray matrix with unchanged dimension when the number of spans increases,which promotes the computation efficiency.Several numerical examples are given,and the present results are compared with the known solutions to illustrate the validity and accurateness of the MRRM for the buckling analysis.

Dynamic quasi-continuum model for plate-type nano-materials and analysis of fundamental frequency

A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials.According to the Hamilton principle,fundamental governing equations in terms of displacement components and angles of rotations are given.As an application of the model,the cylindrical bending deformation of the structure fixed at two ends is analyzed,and a theoretical formula evaluating the fundamental frequency is obtained by using Galerkin's method.Meanwhile,the solution for the classical continuous plate model is also derived,and the size-dependent elastic modulus and Poisson's ratio are taken in computation.The frequencies corresponding to different atomic layers are numerically presented for the plate-type NaC l nano-materials.Furthermore,a molecular dynamics(MD)simulation is conducted with the code LAMMPS.The comparison shows that the present quasi-continuum model is valid,and it may be used as an alternative model,which reflects scale effects in analyzing dynamic behaviors of such plate-type nano-materials.

Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation

This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.

Stretchable,Rehealable,Recyclable,and Reconfigurable Integrated Strain Sensor for Joint Motion and Respiration Monitoring

Cutting-edge technologies of stretchable,skin-mountable,and wearable electronics have attracted tremendous attention recently due to their very wide applications and promising performances.One direction of particular interest is to investigate novel properties in stretchable electronics by exploring multifunctional materials.Here,we report an integrated strain sensing system that is highly stretchable,rehealable,fully recyclable,and reconfigurable.This system consists of dynamic covalent thermoset polyimine as the moldable substrate and encapsulation,eutectic liquid metal alloy as the strain sensing unit and interconnects,and off-the-shelf chip components for measuring and magnifying functions.The device can be attached on different parts of the human body for accurately monitoring joint motion and respiration.Such a strain sensing system provides a reliable,economical,and ecofriendly solution to wearable technologies,with wide applications in health care,prosthetics,robotics,and biomedical devices.

Nonlinear Bending of FCC Nanoplates Based on a Quasi-Continuum Model

A quasi-continuum model of plate-type nanomaterials with the face-centered cubic crystal structures is proposed in this paper.The fundamental governing equations for the nonlinear bending of the nanoplates are given by using the principle of minimum potential energy.Specifically,the analytical solution is derived for cylindrical bending deformation of the structure under uniform transverse loading fixed at two sides based on the modified iterative method.A lattice finite element model is established to verify the present quasi-continuum model.Meanwhile,the corresponding solution by adopting the classical continuous plate theory is presented,in which two cases are considered for use of bulk values(limit values)and nanovalues of both elastic modulus and Poisson's ratio.The difference among the quasi-continuum and continuous models are discussed by computation.