Purpose: As an advanced calculation methodology, reliability-based multidisciplinary design optimization (RBMDO) has been widely acknowledged for the design problems of modern complex engineering systems, not only because of the accurate evaluation of the impact of uncertain factors but also the relatively good balance between economy and safety of performance. However, with the increasing complexity of engineering technology, the proposed RBMDO method gradually cannot effectively solve the higher nonlinear coupled multidisciplinary uncertainty design optimization problems, which limits the engineering application of RBMDO. Many valuable works have been done in the RBMDO field in recent decades to tackle the above challenges. This study is to review these studies systematically, highlight the research opportunities and challenges, and attempt to guide future research efforts.Design/methodology/approach: This study presents a comprehensive review of the RBMDO theory, mainly including the reliability analysis methods of different uncertainties and the decoupling strategies of RBMDO.Findings: First, the multidisciplinary design optimization (MDO) preliminaries are given. The basic MDO concepts and the corresponding mathematical formulas are illustrated. Then, the procedures of three RBMDO methods with different reliability analysis strategies are introduced in detail. These RBMDO methods were proposed for the design optimization problems under different uncertainty types. Furtherly, an optimization problem for a certain operating condition of a turbine runner blade is introduced to illustrate the engineering application of the above method. Finally, three aspects of future challenges for RBMDO, namely, time-varying uncertainty analysis; high-precision surrogate models, and verification, validation and accreditation (VVA) for the model, are discussed followed by the conclusion.Originality/value: The scope of this study is to introduce the RBMDO theory systematically. Three commonly used RBMDO-SORA methods are reviewed comprehensively, including the methods' general procedures and mathematical models.

In this study, the main purpose is to analyze the fatigue failure of thermoplastic polyurethane (TPU) plate under tension-tension load control tests (frequency = 5 Hz, stress ratio = 0.1) and consider the change in hydrogen bond content. The results show that the S-N curve of TPU material shows a downward trend before reaching the fatigue limit (10.25 MPa), and the energy is continuously consumed during the cyclic creep process and undergoes three stages of the hard segment and the soft segment changes. The infrared spectrum study shows that the increase in fatigue life will lead to more physical crosslinking, resulting in the reduction of hydrogen bond content, and the increase in microphase separation, leading to the occurrence of fatigue fracture. In addition, the scanning electron microscope and three-dimensional confocal analysis showed that the crack originated from the aggregation of micropores on the surface of the material and was accompanied by the slip of the molecular chain, the crack propagation direction was at an angle of about 45°.

Bamboo is known as a typical kind of functional gradient natural composite. In this paper, fiber bundles were extracted manually from various parts of the stem in the radial direction, namely the outer, middle, and inner parts. After heat treatment, the mechanical properties of the fiber bundles were studied, including the tensile strength, elastic modulus, and fracture modes. The micromechanical properties of the fiber cell walls were also analyzed. The results showed that the mean tensile strength of the bamboo fiber bundles decreased from 423.29 to 191.61 MPa and the modulus of elasticity increased from 21.29 GPa to 27.43 GPa with the increase in temperature. The elastic modulus and hardness of the fiber cell walls showed a positive correlation with temperature, with the modulus of elasticity and the hardness increasing from 15.96 to 18.70 GPa and 0.36 to 0.47 GPa, respectively. From the outside to the inside of the bamboo stems, the tensile strength and elastic modulus showed a slight decrease. The fracture behavior of the fiber bundles near the outside approximates ductile fracture, while that of the bundles near to the inside tend to be a brittle fracture. The fracture surfaces of the bamboo bundles and the single fibers became smoother after heat treatment. The results show that bamboo fiber bundles distributed near the outside are most suitable for industrial development under heat treatment at 180 °C. Therefore, this study can provide a reasonable scientific basis for the selective utilization, functional optimization, and bionic utilization of bamboo materials, which has very important theoretical and practical significance.

Ultrasonic fatigue tests were performed on Ti60 titanium alloy up to a very high cycle fatigue (VHCF) regime at various stress ratios to investigate the characteristics. The S-N curves showed continuous declining trends with fatigue limits of 400, 144 and 130 MPa at 10⁹ cycles corresponding to stress ratios of R = −1, 0.1 and 0.3, respectively. Fatigue cracks found to be initiated from the subsurface of the specimens in the VHCF regime, especially at high stress ratios. Two modified fatigue life prediction models based on fatigue crack initiation mechanisms for Ti60 titanium alloy in the VHCF regime were developed which showed good agreement with the experimental data.

The materials with grain size gradient variation on the surface, which were prepared with mechanical-induced severe plastic deformation, always show high resistance to high and low cycle fatigue and frictional wear because of their good strength–ductility synergy. The ultrasonic surface rolling treatment (USRT) has the advantages of high processing efficiency, good surface quality, and large residual compressive stress introduced to the surface after treatment. The USRT was used to prepare aluminum alloy (AA7075) samples with a surface gradient structure; meanwhile, the microstructural evolution mechanism of the deformation layers on the gradient structure was studied with XRD, SEM, and TEM. The microstructure with gradient distribution of grain size and dislocation density formed on the surface of AA7075 aluminum alloy after USRT. The surface layer consists of nanocrystals with random orientation distribution, and high-density dislocation cells and subgrains formed in some grains in the subsurface layer, while the center of the material is an undeformed coarse-grained matrix. The results show that the dislocation slip dominates the grain refinement process, following the continuous cutting and refinement of dislocation cells, subgrains, and fragmentation of the second precipitates. This study systematically clarified the mechanism of grain refinement and nanocrystallization on the surface of high-strength aluminum alloys and laid a theoretical foundation for further research on mechanical behavior and surface friction and wear properties of high-strength non-ferrous materials with gradient structure.