This paper proposes an effective couple method for solving reliability-based multi-objective optimization problems of truss structures with static and dynamic constraints. The proposed coupling method integrates a single-loop deterministic method (SLDM) into the nondominated sorting genetic algorithm II (NSGA-II) algorithm to give the so-called SLDM-NSGA-II. Thanks to the advantage of SLDM, the probabilistic constraints are treated as approximating deterministic constraints. And therefore the reliability-based multi-objective optimization problems can be transformed into the deterministic multi-objective optimization problems of which the computational cost is reduced significantly. In these reliability-based multi-objective optimization problems, the conflicting objective functions are to minimize the weight and the displacements of the truss. The design variables are cross-section areas of the bars and contraints include static and dynamic constraints. For reliability analysis, the effect of uncertainty of parameters such as force, added mass in the nodes, material properties and cross-section areas of the bars are taken into account. The effectiveness and reliability of the proposed method are demonstrated through three benchmark-type truss structures including a 10-bar planar truss, a 72-bar spatial truss and a 200-bar planar truss. Moreover, the influence of parameters on the reliability-based Pareto optimal fronts is also carried out.

The paper deals with the multi-objective optimization problems of laminated composite beam structures. The objective function is to minimize the weight of the whole laminated composite beam and maximize the natural frequency. In particular, the simultaneous use of all the design variables such as fiber volume fractions, thickness and fiber orientation angles of layers is conducted, in which the fiber volume fractions are taken as continuous design variables with the constraint on manufacturing process while the thickness and fiber orientation angles are considered as discrete variables. The beam structure is subjected to the constraint in the natural frequency which must be greater than or equal to a predetermined frequency. For free vibration analysis of the structure, the finite element method is used with the two-node Bernoulli-Euler beam element. For solving the multi-objective optimization problem, the nondominated sorting genetic algorithm II (NSGA-II) is employed. The reliability and effectiveness of the proposed approach are demonstrated through three numerical examples by comparing the current results with those of previous studies in the literature.

A cell-based smoothed discrete shear gap method (CS-DSG3) based on the first-order shear deformation theory was recently proposed for static and dynamics analyses of Mindlin plates. In this paper, the CS-DSG3 is extended for analysis and active vibration control of the functionally graded material (FGM) plates integrated with piezoelectric sensors and actuators. In the piezoelectric FGM plates, the properties of core material are assumed to be graded through the thickness by the power law distribution while the electric potential is assumed to be a linear function through the thickness of each piezoelectric sub-layer. A closed-loop control algorithm based on the displacement and velocity feedbacks is used to control static deflection and active vibration of piezoelectric FGM plates. Several numerical examples are conducted to demonstrate the reliability and accuracy of the proposed method compared to other available numerical results.

In this study, a three-dimensional (3D) non-ordinary state-based peridynamics (NOSB-PD) formulation for thermomechanical brittle and ductile fracture is presented. The Johnson-Cook (JC) constitutive and damage model is used to taken into account plastic hardening, thermal softening and fracture. The formulation is validated by considering two benchmark examples: 1) The Taylor-bar impact and 2) the Kalthoff-Winkler tests. The results show good agreements between the numerical simulations and the experimental results.