Journal of Engineering Mechanics

In this paper, improved coupling energies are developed for the vibration analysis of combined structures having coordinate systems in different directions. The in-plane and transverse vibration displacements for the combined structures are expanded as improved Fourier series to ensure the continuity and smoothness of the series representation in the solution domain. The energy principle is adopted to solve the eigenmodes of various combined structures, including the open box coupled structure and enclosed box-type coupled structure. The eigenmodes of the enclosed box-type structure, three-plate coupled structure, and four-plate coupled structure are compared with ones obtained from FEM, and good agreement is observed. The validations of the eigenmodes for the combined structures connected at an arbitrary included angle are analyzed in numerical analysis. The influence of the modal characteristics of the open box structures composed of five plates are studied for different boundary conditions.

Analysis and numerical results are presented for the free asymmetric vibrations of functionally graded (FG) annular nanoplates subjected to nonlinearly varying temperature. The mechanical properties of the plate material were assumed to be temperature-dependent and to vary according to the power-law model in the thickness direction. Because the material is asymmetric in the thickness direction of the nanoplate, the physical neutral plane was obtained and incorporated in the analysis. The governing equations for the presented model were derived using Hamilton’s principle based on first-order shear deformation theory together with Eringen’s nonlocal elasticity theory. Modified size-dependent boundary conditions were derived to handle the paradoxical behavior of the free vibration of nanoplates with a free boundary due to nonlocal parameter and thermal environment. Two different approaches in the quadrature method along with the Chebyshev collocation method were adopted, and it was found that Chebyshev collocation method had a faster rate of convergence than the other two methods. Hence, the Chebyshev collocation method was employed to obtain the numerical values of frequencies. The effect of various parameters together with nonlocal boundary conditions on the nondimensional frequencies was studied. The results were compared with those available in the literature to validate the accuracy of the results and the efficiency of the authors’ technique.

The recently developed singum model was extended to lattice metamaterials and composites for prediction of the effective elasticity based on the stiffness of the lattice components and the structure of the lattice, in which the load is transferred through the lattice network represented by unit cells that can contain one or more singums. The equilibrium of the singums was considered under a displacement variation, and the relation between the variations of averaged stress and strain can be evaluated to predict the elasticity. It was proved that the stiffness of any unit cells is the same as that of the primitive cell. A generalized formulation was developed to calculate the effective elasticity of lattice metamaterials and composites, which reflects the symmetry and anisotropic feature of the lattice more accurately. A hydrostatic load does not change the shape of the singum but changes its elasticity, although the bonds are linear elastic. The formulation shows the prestress-dependent elasticity for lattice metamaterials. When a large uniform biaxial tension is applied, a honeycomb lattice can exhibit a negative Poisson’s ratio under a pre-tension. Case studies of auxetic and body-centered cubic lattices were conducted to demonstrate the negative Poisson’s ratio and anisotropic elasticity, respectively.

Adaptive sampling near a limit state is important for metamodeling-based reliability analysis of structures involving an implicit limit state function. Active learning based on the posterior mean and standard deviation provided by a chosen metamodel is widely used for such adaptive sampling. Most studies on active learning-based reliability estimation methods use the Kriging approach, which provides prediction along with its variance. As with the Kriging approach, sparse Bayesian learning-based regression also provides posterior mean and standard deviation. Due to the sparsity involved in learning, it is expected to be computationally faster than the Kriging approach. Motivated by this, active learning-enhanced adaptive sampling-based sparse Bayesian regression is explored in the present study for reliability analysis. In doing so, polynomial basis functions, which do not involve free parameters, are chosen for the sparse Bayesian regression to avoid computationally expensive parameter tuning. The convergence of the proposed approach is attained based on the stabilization of 10 consecutive failure estimates. The effectiveness of the proposed adaptive sparse Bayesian regression approach is illustrated numerically with five examples.