Galerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate functionally graded material (FGM) close to reality. Mathematical formulations concern the Timoshenko shear deformation theory. Small scale and atomic interactions are shaped as maintained by the nonlocal strain gradient elasticity approach. Since there is no bifurcation point for FGMs, whenever both boundary conditions are rotational and the neutral surface does not match the mid-plane, the clamp configuration is examined only. The fourth-order ordinary differential stability equations will be converted into the sets of algebraic ones utilizing the GWRM whose accuracy was proved before. After that, by simply solving the achieved polynomial constitutive relation, the parametric study can be started due to various predominant and overriding factors. It was found that the flexomagneticity is further visible if the ferric nanobeam is constructed by FGM technology. In addition to this, shear deformations are also efficacious to make the FM detectable.

伽辽金加权残差法 (GWRM) 被应用和实施以解决热环境中包含弯曲磁性的功能梯度压电结构的轴向稳定性和分叉点。连续体样本涉及分布在具有恒定方形横截面的异质介质中的指数质量。研究物理中性平面以假设功能梯度材料 (FGM) 接近现实。数学公式涉及 Timoshenko 剪切变形理论。小尺度和原子相互作用的形状由非局部应变梯度弹性方法维持。由于 FGM 没有分叉点，当两个边界条件都是旋转的且中性表面与中平面不匹配时，仅检查夹具配置。四阶常微分稳定性方程将利用之前已经证明其准确性的GWRM转换为代数方程组。之后，通过简单地求解获得的多项式本构关系，参数研究可以由于各种主要和压倒一切的因素而开始。研究发现，如果通过 FGM 技术构建铁纳米束，则挠曲磁性更加明显。除此之外，剪切变形也可以有效地使 FM 可检测。研究发现，如果通过 FGM 技术构建铁纳米束，则挠曲磁性更加明显。除此之外，剪切变形也可以有效地使 FM 可检测。研究发现，如果通过 FGM 技术构建铁纳米束，则挠曲磁性更加明显。除此之外，剪切变形也可以有效地使 FM 可检测。