Mechanical structures always bear multiple loads under working conditions. Topology optimization in multi-load cases is always treated as a multi-objective optimization problem, which is solved by the weighted sum method. However, different weight factor allocation strategies have led to discrepant optimization results, and when ill loading case problems appear, some unreasonable results are obtained by those alternatives. Moreover, many multi-objective optimization problems have certain optimization objective, and an evaluation formula to measure Pareto solution in the multi-objective optimization problem area is lacking. Regarding these two problems, a new method for calculating the weight factor is proposed based on the definition of load case severity degree. Additionally, an amplified load increment is derived and suggested in the minimum compliance with a volume constraint problem. Ideality is formulized from Pareto front to the ideal solution to evaluate the different optimization results. Benchmark topology optimization examples are solved and discussed. The results show that the load case severity degree is less affected by the different weighted sum functions and can avoid ill loading case phenomena, and the ideality of optimization result obtained by the load case severity degree is the best.

Biological structures have excellent mechanical performances including lightweight, high stiffness, etc. However, these are difficult to apply directly to some given complex structures, such as automobile frame, control arm, etc. In this study, a novel bionic design method for skeleton structures with complex features is proposed by the bio-inspired idea of “main-branch and sub-branch”. The envelope model of a given part is established by analyzing the structural functions and working conditions, and the load path is extracted by the load-transferred law as the structural main-branch. Then, the selection criterion of bionic prototype is established from three aspects: load similarity, structural similarity and manufacturability. The cross-sections with high similarities are selected as the structural sub-branch. Finally, the multi-objective size optimization is carried out and a new model is established. The bionic design of a control arm is carried out by the method: structural main-branch is obtained by the load path analysis and structural sub-branch is occupied by the fish-bone structure. The design result shows that the structural stiffness is increased by 62.3%, while the weight is reduced by 24.75%. The method can also be used for other fields including automobile, aerospace and civil engineering.

The topology optimization of dynamic stress constraints is highly nonlinear and singular and has been little studied. Dynamic stress based on progressive structural optimization is only available by applying the modal iteration method, but due to the nonlinear limitations of the modal superposition method, there is an urgent need to develop a progressive structural optimization method based on dynamic stress sensitivity under direct integration. This method is for the dynamic stresses under non-periodic loading with iterative cycle updating variations. This article proposes a topological optimization method of continuum structures with stress constraints under an aperiodic load based on the Bi-directional Evolutionary Structural Optimization Method (BESO). First, the P-norm condensation function was used to obtain the global stress to approximate maximum stress. By introducing the Lagrange multiplier, the design goal was to increase the P-norm stress on the basis of the smallest volume. After that, based on the dynamic finite element theory, the sensitivity of each cell formula of the objective function and the constraint conditions of the design variables were strictly derived. Then, the performance evaluation index was put forward based on volume and stress, and the convergence criterion based on the performance evaluation index was defined. This method solves the topology optimization problem of stress constraints under a non-periodic load and the topology optimization problem of stress constraints under a periodic load, such as a simple harmonic load.

In this study, we focus on the new energy-absorbing lattice cell configuration designed by topology optimization. To address the difficulty involved in the quantitative description of densification in periodic lattice plastic deformation, in this study, we propose characterizing the plastic densification state of a porous structure with the maximum ratio of two adjacent equivalent plastic moduli in the nonlinear static analysis process. Then, dynamic topology optimization is carried out with the maximization of the absorbed energy as the objective and the densification strain as the constraint to obtain the new topological configuration of the energy-absorbing lattice cell. Finally, additive manufacturing and quasistatic testing of the new energy-absorbing lattice structure and body-centered cubic and face-centered cubic lattice structure is conducted. The results show that, under the same conditions, the strain energy absorbed by the energy-absorbing lattice is approximately 3.5 times that absorbed by the body-centered cubic structure and 2.8 times that absorbed by the face-centered lattice structure with a low impact speed of 5 m/s.

In this paper, the O-shaped plate with different materials are used to analyze their natural frequencies at different boundaries and different plate thicknesses and the forced response under the action of point forces. By the improved Fourier series method, the discontinuity of coupling system at all boundaries in the overall solution domain is overcame. Through the energy principle and the Rayleigh-Ritz technology, the matrix equation of the system governing equations can be obtained. In addition, based on various materials, boundary conditions and thicknesses, some new results have been demonstrated, which may become the foundation for the future research.