The influence of soil heterogeneity is studied on the bending of circular thin plates using two modified Vlasov foundation models. The model parameters are determined reasonably using an iterative technique. According to the principle of minimum potential energy and considering transversely isotropic soils and Gibson soils, the governing differential equations and boundary conditions for circular thin plates on two modified Vlasov foundations are derived using a variational approach, respectively. The determination of attenuation parameters is a difficult problem, which has hindered the further application of the Vlasov foundation model. The equation that must be satisfied by the attenuation parameter is determined, and an iterative method is used to solve the problem. A comparative analysis is conducted between two modified Vlasov models and the traditional Vlasov model. The results show that the governing equations and boundary conditions for circular thin plates resting on two modified foundations are consistent with those for a circular thin plate on traditional two-parameter foundation after degradation. The accuracy and reliability of the proposed solutions are demonstrated by comparing the obtained results with those reported in the literature. The heterogeneity of soils, including the transversely isotropic soils and Gibson soils, has a certain effect on characteristic parameters of the foundation models as well as the deformations and internal forces of circular thin plates. The present study could be employed as a reference for future engineering designs.

中文翻译：

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使用两种修正的Vlasov模型的弹性基础上的圆形薄板弯曲分析

使用两个改进的Vlasov基础模型研究了土壤异质性对圆形薄板弯曲的影响。使用迭代技术合理地确定模型参数。根据最小势能原理，并考虑横观各向同性土壤和吉布森土壤，分别采用变分方法推导了两个修正的Vlasov基础上圆形薄板的控制微分方程和边界条件。衰减参数的确定是一个难题，阻碍了Vlasov基础模型的进一步应用。确定了衰减参数必须满足的方程，并使用迭代方法来解决该问题。在两个修改后的Vlasov模型和传统Vlasov模型之间进行了比较分析。结果表明，在两个修改的基础上放置的圆形薄板的控制方程和边界条件与退化后传统的两参数基础上的圆形薄板的控制方程和边界条件是一致的。通过将获得的结果与文献中报道的结果进行比较，可以证明所提出解决方案的准确性和可靠性。包括横观各向同性土壤和吉布森土壤在内的土壤异质性对基础模型的特征参数以及圆形薄板的变形和内力都有一定的影响。本研究可以作为未来工程设计的参考。结果表明，在两个修改的基础上放置的圆形薄板的控制方程和边界条件与退化后传统的两参数基础上的圆形薄板的控制方程和边界条件是一致的。通过将获得的结果与文献中报道的结果进行比较，可以证明所提出解决方案的准确性和可靠性。包括横观各向同性土壤和吉布森土壤在内的土壤异质性对基础模型的特征参数以及圆形薄板的变形和内力都有一定的影响。本研究可以作为未来工程设计的参考。结果表明，在两个修改的基础上放置的圆形薄板的控制方程和边界条件与退化后传统的两参数基础上的圆形薄板的控制方程和边界条件是一致的。通过将获得的结果与文献报道的结果进行比较，可以证明所提出解决方案的准确性和可靠性。包括横观各向同性土壤和吉布森土壤在内的土壤异质性对基础模型的特征参数以及圆形薄板的变形和内力都有一定的影响。本研究可以作为未来工程设计的参考。