On torsion of nonlocal Lam strain gradient FG elastic beams

Abstract The nonlocal strain gradient theory of elasticity is the focus of numerous studies in literature. Eringen's nonlocal integral convolution and Lam's strain gradient model are unified by a variational methodology which leads to well-posed structural problems of technical interest. The proposed nonlocal Lam strain gradient approach is presented for functionally graded (FG) beams under torsion. Static and dynamic responses are shown to be significantly affected by size effects that are assessed in terms of nonlocal and gradient length parameters. Analytical elastic rotations and natural frequencies are established by making recourse to a simple solution procedure which is based on equivalence between integral convolutions and differential equations supplemented with variationally consistent (but non-standard) nonlocal boundary conditions. Effects of Eringen's nonlocal parameter and stretch and rotation gradient parameters on the torsional behavior of FG nano-beams are examined and compared with outcomes in literature. The illustrated methodology is able to efficiently model both stiffening and softening torsional responses of modern composite nano-structures by suitably tuning the small-scale parameters

Axial and Torsional Free Vibrations of Elastic Nano-Beams by Stress-Driven Two-Phase Elasticity

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter. Effectiveness of stress-driven mixture is illustrated by analyzing axial and torsional free vibrations of cantilever and doubly clamped nano-beams. The local/nonlocal integral mixture is conveniently replaced with an equivalent differential law equipped with higher-order constitutive boundary conditions. Exact solutions of fundamental natural frequencies associated with strain- and stress-driven mixtures are evaluated and compared with counterpart results obtained by strain gradient elasticity theory. The provided new numerical benchmarks can be effectively employed for modelling and design of Nano-Electro-Mechanical-Systems (NEMS)

A Note on the Inverse Reconstruction of Residual Fields in Surface Peened Plates

Abstract A modified stress function approach is developed here to reconstruct induced stress, residual stress and eigenstrain fields from limited experimental measurements. The present approach is successfully applied to three experimental measurements set in surface peened plates with shallow shot peening affected zone. The well-rehearsed advantage of the proposed approach is that it not only minimizes the deviation of measurements from its approximations but also will result in an inverse solution satisfying a full range of continuum mechanics requirements. Also, the effect of component thickness as a geometric parameter influencing the residual stress state is comprehensively studied. A key finding of present study is that the plate thickness has no influence on the maximum magnitude of eigenstrain profile and compressive residual stresses within the shot peening affected zone while having a great influence on the magnitude of tensile residual stress and the gradient of linear residual stresses present in deeper regions