Variable Density Method Based On Density-Volume Interpolation And Its Application In Designing The Beam Of Hydraulic Press

Topology optimization of continuum structures is one of the hotspots and difficult issues in the field of structural optimization.Compared with size optimization and shape optimization,topology optimization studies the layout of structural materials and fundamentally guides the design of structural layouts thus it has more obvious benefits.It is of great engineering significance to study the topology optimization of the large and medium-sized hydraulic press beams which are large-sized and high-weight complex structures.This paper studies the material interpolation model and proposes a density-volume interpolation model.The principle is to achieve the penalty of intermediate density by constructing a penalty relationship between density and volume.Through the Hashin-Shtrikman modulus boundary of the two-phase composite material,the value range of the penalty factors are obtained when the density-volume interpolation model is expressed as a composite material consisting of solid and void.The numerical example shows that the density-volume interpolation model can get a larger penalty than the density-stiffness interpolation model.Based on the density-volume interpolation model,the mathematical model of topology optimization is established to minimize the structure volume under multi-displacement constraints.Based on the Kuhn-Tucker optimal condition,the calculation process of optimality criterion method is derived.And the solution method of Lagrange multipliers for multi-displacement constrained problem is obtained by liner approximation treatment of the displacement constraints.For the problem of numerical instability and gray elements in the topology optimization process,two new suppression strategies are proposed.One strategy is sensitivity filtering combined with grayscale suppression.A suppression method for gray elements based on contrast enhancement is constructed.By introducing contrast enhancement operators in iterations to drive the intermediate densities to two boundaries and combining with sensitivity filtering,the problem of numerical instability and gray elements are achieved.The other strategy is a new bilateral filtering method based on cross template.This method is based on the cross-shaped filter template,and the average density of the elements which are located in the same branch is taken into consideration when setting the gray weight function.A continuous change method is adopted for the parameter setting of the gray weight function.The two suppression strategies are verified by numerical examples.Based on the above research,a structural topology optimization system for minimizing weight under displacement constraints was developed by using the finite element analysis platform MSC.MARC.This system is used to optimize the structure of a 30 MN hydraulic press upper beam and the weight of the optimized beam is 29.8% less than that of the original traditional upper beam.It not only realizes lightweight of beam structure,but also obtains a novel beam structure.The scaled experiment results show that the stress distribution of the structure is more uniform,and the stiffness and strength indicators all meet the design requirements.