The beam of drainage plate bending machine bears two-way variable loads in operation. The vibration resistance and rigidity of beam are the main factors that affect accuracy and stability of the whole machine. The stress analysis of beam was carried on firstly in the paper, and then the mathematical model of topology optimization based on variable density method was established in which an additional constraint condition was taken part in. The iterative formula is deduced taking advantage of optimality criteria method and Lagrange multiplier is calculated using volume constraint. A filtering function is imported in order to solve checkerboard and mesh-independent. After the preparation of MATLAB program, 3D model was created with using the optimized cross section shape. Static stiffness and dynamic characteristics have been analyzed to obtain the deformation, stress cloud charts and natural frequency to improve rigidity and avoid resonance. Besides a vibration experiment was performed by applying the LMS Test.lab Vibration testing and analysis system. The results are highly compatible to prove the accuracy and efficiency of the optimization and simulation. The final results were applied to the beam design of drainage plate bending machine and provide helpful instruction for similar optimization design.%屋顶排水槽板折弯机的横梁在折弯过程中承受双向载荷作用,横梁的刚性和抗振性是影响折弯机整机精度和稳定性的重要因素.首先对横梁承载情况进行受力分析,然后建立基于变密度法的拓扑优化数学模型,增加双向载荷约束条件,采用通用性较强的优化准则法,通过卷积算子建立滤波器修改元素灵敏度以提高网格独立性,解决棋盘格和网络依赖性问题,编制相应MATLAB优化程序进行结构拓扑优化,利用优化后的截面形状绘制三维模型,引入到ANAYS软件对拓扑结构优化结果进行静动态分析以验证优化结果,并通过LMS振动测试仪和分析系统对横梁进行模态测试试验,验证了优化与仿真的有效性和准确性,最终设计成果应用于屋顶排水槽板折弯机横梁设计,取得了很好的工程应用效果,为相似结构件优化设计提供了有益的借鉴与参考.
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