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In this paper, meshfree simulations of large deformation of thin shell structures is presented. It has been shown that the window function based meshfree interpolants can be used to construct highly smoothed (high order``manifold'') shape functions for three-dimensional (3-D) meshfree discretization/interpolation, which can be used to simulate large deformation of thin shell structures while avoiding ill-conditioning as well as stiffening in numerical computations.The main advantage of such 3-D meshfree continuum approach is its simplicity in both formulation and implementation as compared to shell theory approach, or degenerated continuum approach. Moreover, it is believed that the accuracy of the computation may increase because of using 3-D exact formulation. Possible mechanism to relieve shear/volumetric locking due to the meshfree interpolation is discussed. Several examples have been computed by using a meshfree, explicit, total Lagrangian formulation. Towards to developing a self-contact algorithm, a novel meshfree contact algorithm is proposed in the end.

Reproducing Kernel Particle Methods (RKPM) with a built-in feature of multiresolution analysis are addressed. Some fundamental concepts such as reproducing conditions, and correction function are constructed to systematize the framework of RKPM. In particular, Fourier analysis, as a tool, is exploited to further elaborate RKPM in the frequency domain. Furthermore, we address error estimation and convergence properties. We present several applications which con®rm the widespread applicability of multiresolution RKPM.

In this Letter, we report the experimental observations of a tunable curved photonic nanojet (photonic hook) generated by a 5 µm polydimethylsiloxane microcylinder deposited on a silicon substrate and illuminated by 405 nm laser beam. A moveable opaque aluminum-mask is mounted in front of the microcylinder implementing partial illumination and imparting spatial curvature to the photonic nanojet. Experimental results of main parameters (tilt angle, width, and intensity) of emerging photonic hooks exhibit close agreement with numerical predictions of the near-field optical structures. The experimentally measured full widths at half-maximum of photonic hooks are 0.48 λ , 0.56 λ , and 0.76 λ for tilt angles of θ = 0 ∘ , 5.7°, and 20.1°, respectively. Photonic hooks possess great potential in complex manipulation such as super-resolution imaging, surface fabrication, and optomechanical manipulation along curved trajectories.

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