A nonlocal theory is presented for the bending in large deformations under applied loads of an initially straight rod. This has similarities with the classical Euler’s elastica in the sense that the bending stiffness remains homogeneously constant, but it depends on an integral average of the entire curvature field. The discretized form of the equilibrium equations is identical to those governing the response of structural systems already called flexural tensegrity beams, composed of a chain of segments in unilateral contact, whose integrity under flexion is due to prestressing tendons and to the shape of the contact surfaces. An analytical method of solution is proposed modulo the calculation of elliptic integrals, which is compared in paradigmatic examples with the numerical approach, or with an approximation of the curvature field with shape functions. The comparison between the continuum theory and the discrete case of flexural tensegrity highlights the physical role of the constitutive parameters, paving the way for a tailored design of innovative devices and the modelling of complex biological structures, based on the capability of transforming the mechanical properties with very small changes at the level of the underlying micro-constituents.

提出了一种非局部理论，用于在初始直杆施加的载荷下大变形时的弯曲。在弯曲刚度保持均匀恒定的意义上，这与经典的欧拉弹性体有相似之处，但它取决于整个曲率场的积分平均值。平衡方程的离散形式与支配已称为挠性张紧梁的结构系统的响应相同，后者由单侧接触的链段链组成，其屈曲下的完整性归因于预应力筋和接触面的形状。提出了一种以椭圆积分计算为模的解的解析方法，并在范例中与数值方法进行了比较，或具有形状函数的曲率场近似值。连续性理论与弯曲张力离散情况之间的比较突出了本构参数的物理作用，为基于创新的机械性能转化能力的量身定制的创新设备设计和复杂生物结构建模铺平了道路。潜在的微成分水平上的变化很小。