Section optimum design of continuous structures based on full stress criterion

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (18) : 250-257.

WU Shan, HE Haoxiang, ZHOU Yujing

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Abstract

The current continuum optimization design mainly focuses on local optimization and material topology optimization, and the feasibility of its engineering application is insufficient.In addition, in the full stress optimization design, the complex load patterns and material nonlinearity are not comprehensively considered.Hence, the traditional methods are difficult to directly guide the structural elastic-plastic optimization design.It is of great theoretical and engineering value to explore theoretical methods and analytical solutions for the optimization of section and shape of continuum based on the mechanical characteristics, geometric shape and load pattern of engineering structures.In the study, engineering structures were regarded as continuous cantilever beams with variable cross-section, and the complex loads such as wind and seismic excitation were simplified as one of three load distribution patterns including uniform load, inverted triangle load and inertia force-related load.According to the concept of full stress, the optimization objective of the structure with typical cross sections such as circular and box shapes is set as that with the same or similar normal stress along the height direction.The section optimization theory and analytical form for optimal continuous structures were explored through establishing different representation forms of section bending moments and considering material nonlinearity.Furthermore, the analytical expression of the optimal stiffness distribution of the structure was given.The example results show that the full stress criterion can be realized in both the elastic and plastic stages when the section size is designed according to the analytical results.The optimization results are effective under both static and dynamic loads.The optimal section size distribution and the optimal stiffness distribution are different for various load patterns and section types, so,the specific continuum optimization design for engineering structures should be carried out according to specific engineering requirements.

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full stress / equal stress / optimal design / nonlinear constitutive / load pattern / stiffness distribution

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WU Shan, HE Haoxiang, ZHOU Yujing. Section optimum design of continuous structures based on full stress criterion[J]. Journal of Vibration and Shock, 2021, 40(18): 250-257

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