Free‐form grid structure is a kind of structure whose shape cannot be expressed by analytical functions. Although this kind of structure has been widely used in practice, how to generate the structural shapes that not only satisfy architectural requirements but also have excellent mechanical properties is still a problem. This article focuses on the shape generation of complex grid structures and proposes a novel shape‐generation method for free‐form grid structures. The method integrates numerical inverse hanging method and multiobjective optimization. First, it uses numerical inverse hanging method to generate structural shapes in low bending moment level. Next, it uses dynamic weight multiobjective firefly optimization algorithm to adjust the parameters of the inverse hanging method adaptively so that the structural shape can satisfy architectural requirements. Comparisons with former shape‐generation methods show that the proposed method is more effective. Numerical examples based on real structures illustrate the applicability of the proposed method in practice.

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We observe sharp step-down discontinuities in the magnetic susceptibility of NH4H2PO4 and NH4H2PO4-d 60 (60% deuterated) along the a- and c-axes occurring exactly at their antiferroelectric transition temperatures. For the case of KH2PO4, less pronounced discontinuities occur at the ferroelectric transition temperature. To explain this, we treat the acid protons as individual oscillators that generate current elements that translate to magnetic forces in near resonance with each other. With decreasing temperature, the resonant forces become more commensurate, which amplifies a disproportionate drop off of two types of magnetic forces to eventually trigger the structural phase transitions. For the case of NH4H2PO4, the associated internal magnetic field appears to aid the NH4 + to order at a higher temperature. At 49 K, a shoulder-like anomaly in both NH4H2PO4 and KH2PO4 is attributed to a possible onset of macroscopic quantum tunneling of protons. Our findings bring forth a new category of intrinsic multiferroic systems.