SUMMARYOptimal hybrid stress quadrilaterals can be obtained by adopting appropriate stresses and displacements, and satisfying the energy compatibility condition is shown to be an ultimate key to obtaining optimal stress modes. By using compatible isoparametric bilinear (Q 4 ) displacements and 5-parameter energy compatible stresses of the combined hybrid ÿnite element CH(0-1), a robust 4-node plane stress element ECQ 4 is derived. Equivalence to another hybrid stress element LQ 6 with 9-parameter complete linear stresses based on a modiÿed Hellinger-Reissner principle is established. A convergence analysis is given and numerical experiments show that elements ECQ 4 \LQ 6 have high performance, i.e. are accurate at coarse meshes, insensitive to mesh distortions and free from locking.

No abstract

No abstract

Topological defects with symmetry-breaking phase transitions have captured much attention.Vortex generated by topological defects exhibits exotic properties and its flow direction can be switched by altering the spin configurations. Contrary to electromagnetic and acoustic domains, the topological transport of elastic waves in periodic structures with topological defects is not well explored due to the mode conversion between the longitudinal and transverse modes. Here, we propose an elastic topological insulator with spontaneously broken symmetry based on the topological theory of defects and homotopy theory. Multiple topological transitions for elastic waves are achieved by topologically modifying the ellipse orientation in a triangular lattice of elliptical cylinders. The solid system, independent of the number of molecules in order parameter space, breaks through the limit of the point-group symmetry to emulate elastic pseudospin-orbit coupling. The transport robustness of the edge states is experimentally demonstrated. Our approach provides new possibilities for controlling and transporting elastic waves.Topological defects in ordered media [1] with spontaneously broken symmetry have attracted an enormous interest due to their nontrivial topology, which can play a central role in physical processes such as phase transitions [2][3][4]. Their topological origin and fundamental behavior was first described by the Kibble-Zurek mechanism as a continuous system is quenched across a phase transition into an ordered state [5,6]. In recent years, such topological defects have been extensively studied in various branches of physics. It has been shown that the topological defects with +1/2 or -1/2 topological charge can govern cell motion [7][8][9], and even arise in fatigue of materials [10]. Antivortices and vortices can be generated in three-dimensional nonporous ferroelectric structures with topological defects [11]. These exotic physical phenomena and unprecedented material properties imply that topological defects can be leveraged to explore quantum behavior of classical waves and new forms of topological orders in

Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.