In this article, we propose a fast method to solve large-scale three-dimensional topology optimization problems subject to buckling constraints. Buckling analysis entails the solution of a generalized eigenvalue problem. For problems with large degrees of freedom, the current numerical methods tend to be memory-hungry, leading to high computational costs. First, a low-memory assembly-free linear buckling analysis method is proposed. Specifically, this method is based on the voxelization model, an assembly-free version of the deflated conjugate gradient is used to accelerate the iteration solution of linear systems of equations, where neither the stiffness matrix nor the deflation matrix is assembled, and the parallelization of matrix-vector multiplication is achieved by the congruency of voxels. Due to the particularity of the stress stiffness matrix in the buckling analysis, the inverse iteration is used to solve the general eigenvalue problem, which can reduce the operations of stress stiffness matrix considerably. Based on the efficient buckling analysis method, we extend the level-set method for buckling constraints in a semi-analytical manner. Several numerical experiments demonstrate that the proposed method can solve large-scale three-dimensional buckling analysis and topology optimization against buckling constraints effectively.

Linear buckling analysis entails the solution of a generalized eigenvalue problem. Popular methods for solving such problems tend to be memory-hungry, and therefore slow for large degrees of freedom. The main contribution of this paper is a low-memory assembly-free linear buckling analysis method. In particular, we employ the classic inverse iteration, in conjunction with an assembly-free deflated linear solver. The resulting implementation is simple, fast and particularly well suited for parallelization. The proposed method is used here to solve large scale 3D topology optimization problems subject to buckling constraints, where buckling problems must be solved repeatedly.

In this paper, the structural, electronic and optical absorption properties of [Formula: see text]-aminobenzoic acid crystals (hereinafter referred to as [Formula: see text]-amino) in the pressure range of 0–300[Formula: see text]GPa are calculated by density functional theory (DFT). The changing trend of the lattice constant of [Formula: see text]-amino under different pressures is analyzed. We find that the crystal undergoes complex transformation. Furthermore, it can be seen that the structure of [Formula: see text]-amino along the [Formula: see text]-axis is stiffer than that along the [Formula: see text]-axis and [Formula: see text]-axis, suggesting that the crystal has anisotropic compressibility. Through the analysis of the band gap and density of states of [Formula: see text]-amino, it is found that the electronic properties of [Formula: see text]-amino are transformed from semiconductor phase to metal phase at 100[Formula: see text]GPa, then jump into the semiconductor phase and maintain the metal phase again in the pressure range of 150–250[Formula: see text]GPa. Repeated phase transitions indicate that the structure of [Formula: see text]-amino becomes more unstable as the pressure increases. Besides, from the absorption spectra, the optical activity of [Formula: see text]-amino is relatively high with the increase of pressure, and two obvious structural transitions are observed at 70 and 270[Formula: see text]GPa, respectively.

Usually the gear modification is a main measure to reduce the vibration and noise of the gears, but in view of the complexity of the gear modification, topology optimization method was used to optimize the structure of the gear. The minimum volume was set as the direct optimization goal. To achieve the target of reducing contact stress, tooth root bending stress and improving flexibility, the upper bound of the stress and lower bound of the flexibility were set appropriately, thus realizing multi-objective optimization indirectly. A method for converting topology result into parametric CAD model which can be modified was presented, by fitting the topology result with simple straight lines and arcs, the model can be smoothed automatically, after further regulating, the geometry reconstruction was finished. After topology optimization, the resulting structure and properties of the gear are consistent with cavity gear. While reducing the weight of the gear, the noise can be reduced and its life would be extended through increasing flexibility and reducing tooth root stress.

A low power and high performance voltage controlled oscillator (VCO) is designed by 0.18µm CMOS process. The output is stable, output frequency of the VCO has high linearity, and can be changed by regulation the voltage of input control pin VT. The output frequency is from 200 to 500MHz, and the operation voltage is from 1.2V to 3.3V. The operation current is only 2.5mA and Anti-interference ability has improved by using current hunger type ring oscillator. Between -40 to 125℃, the Linear Rate of central frequency is only 0.2%. The final chip size is only 200µm X100µm.