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A novel method for load bounds identification for uncertain structures is proposed in the frequency domain. The uncertain parameters are assumed to locate in their intervals and only their bounds rather than their precise information are needed. To quantitatively describe the effect of the interval uncertainty on the load identification in the frequency ranges, the interval extension is then introduced in the frequency response function (FRF)-based least squares approach. Therefore, the load bounds are determined through the summation of the two separate parts including the midpoint part and the perturbed part of the load. The midpoint part is computed by using the Moore–Penrose pseudo-inversion and the perturbed part is transformed into the first derivatives of the midpoint load with respect to the uncertain parameters by applying the truncated total least squares (TTLS). Two numerical examples are investigated to validate that the proposed method is very effective to predict the load bounds for the uncertain structure in frequency domain.

This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the multi-scale concurrent topology optimization (CTO) framework. To describe the imprecise probabilistic uncertainty efficiently, the type I hybrid interval random model is adopted. An improved hybrid perturbation analysis (IHPA) method is formulated to estimate the expectation and stand variance of the objective function in the worst case. Combined with the bi-directional evolutionary structural optimization (BESO) framework, the robust designs of the structure and its composite material are carried out. Several 2D and 3D numerical examples are presented to illustrate the effectiveness of the proposed method. The results show that the proposed method has high efficiency and low precision loss. In addition, the proposed RCTO approach remains efficient in both of linear static and dynamic structures, which shows its extensive adaptability.where J Y and J Y denote the lower and upper bounds of interval vector J Y . The symbol m J Y is the mean value of J Y , which can be calculated by averaging the lower and upper bounds value as shown in Eq. (16b). I J Y denotes the variation interval of J Y , which depends on the difference of the lower and upper bound values as shown in Eq. (16c). The deviation J Y  of the symmetrical interval can be acquired by averaging the upper and lower bounds of J Y as shown in Eq. (16d). In the combined form, the J-th hybrid interval random parameter( ) JJ X Y can be formulated as RCTO Volume fraction of solid: 95.6% Volume fraction of Phase 1: 70.3% DCTO Volume fraction of solid: 95.1% Volume fraction of phase 1: 70.7% 33 (b) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 93.0% Volume fraction of phase 1: 72.4% DCTO Volume fraction of solid: 92.7% Volume fraction of phase 1: 72.7% (c) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 90.4% Volume fraction of phase 1: 74.9% DCTO Volume fraction of solid: 88.9% Volume fraction of phase 1: 76.3%JJ J ee JJ J J J J e J J e J J JJ J e e J J J J J J J J e J J e 2 2 J J J J JK J e e J J J J J J J J J J J J J e J J JJ JJ e J J J J JJ J J e J J J J e JJ e J J J J 3m d I e J J J J x X X e J J e J J e J J e J J e J J e J J e e e e J J J J e J J J J e J J J J H T A a J J J J H a J J J J pT A J J J J A e J J J J A e J J J J J J J J a i A Y J J J J p a i A Y J J J J a i J J J J a i A Y J J J J p a i A Y J J J J Ne ia A i J J J J a i J J J J Ne ia A i J J J J

In this work, resonant structures (RSs) are embedded in the resin matrix to form the micro-scale artificial composite materials to mitigate the blast wave with a very wide frequency range (BWR). The propagation of stress waves in the resin and composite materials is described, and the composite materials exhibit stronger blast wave attenuation characteristic compared with the pure resin material. The attenuation mechanism of the composite materials is explained in detail through the absorption, storage and conversion of impact energy. In addition, the influences of materials of the RSs on the performances of the composite materials are analyzed, and the RS is redesigned to further improve the attenuation effect of the composite material. Equivalent model of the composite material is first proposed and established based on the weakly nonlinear lattice system (WNLS). At the same time, artificial tree algorithm is applied to design its spring stiffness parameters. Based on the WNLS, a three-dimensional composite material plate structure is built to mitigate the overpressure of blast wave at the macro-scale. Compared with traditional materials, the composite material exhibits superior attenuation effect and greater lightweight.

A non-contact acoustic pressure-based method is proposed for load identification in the acoustic structure interaction system involving non-probabilistic uncertainty. The forward problem for load identification is established through the discretized convolution integral relationship of the dynamic loads and the Green's kernel function matrix of the system. The inverse process is constructed by using truncated single value decomposition approach in order to overcome the ill-posedness of the global kernel function matrix. In this work, two non-probabilistic models including ellipsoid model and interval model are proposed to quantify the effects of the system uncertainty. Several numerical examples are investigated to verify the effectiveness of the present methods. The results show that the non-contact acoustic pressure-based method with great convenience for dynamic load identification is accurate and effective. For the system with non-probabilistic uncertainty, the ellipsoid model and interval model are the proper choices to identify the bounds with knowing only the extreme values of the parameters. Moreover, the load bounds derived from the ellipsoid model are more reliable than those derived from the interval model.