The paper proposes the sequential elastic analyses run within the node-based smoothed finite element (NS-FE) framework incorporating an automatic adaptive mesh scheme to converge the lower-bound collapse load limit of plane-strain structures. The approach is familiar to practical designers as it solely involves a series of linear elastic analysis solves. Each of which performs a modified version of elastic compensation method that appropriately considers the modulus variations of some critical members. The nonlinear constitutive formulations describing intrinsic material properties can be directly accommodated. The NS-FE method simply adopts the low-order displacement functions, whilst the mesh adaptive algorithm employs the newest-bisection criteria with the novel modulus variation error indicators. A number of numerical examples and benchmarks involving the plane-strain structures with vertex and curve geometries illustrate the accuracy and efficiency of the proposed method. The approach overcomes the challenges associated with stress singularity and volumetric locking phenomena in an incompressibility condition. The collapse load solution converges to the lower-bound limit at modest computing efforts, where the final NS-FE layout (namely fine meshes over the areas developing high modulus variation rates and at the same time coarse meshes for those undergoing elasticity) depicts the failure lines of structures and hence mechanisms.

本文提出了在基于节点的平滑有限元 (NS-FE) 框架内运行的顺序弹性分析，该框架结合了自动自适应网格方案，以收敛平面应变结构的下限坍塌载荷限制。该方法对实际设计人员来说很熟悉，因为它只涉及一系列线弹性分析求解。每个都执行弹性补偿方法的修改版本，该方法适当地考虑了一些关键构件的模量变化。可以直接适应描述固有材料特性的非线性本构公式。NS-FE 方法简单地采用低阶位移函数，而网格自适应算法采用最新的二分准则和新颖的模量变化误差指标。许多涉及具有顶点和曲线几何形状的平面应变结构的数值例子和基准说明了所提出方法的准确性和效率。该方法克服了在不可压缩条件下与应力奇异性和体积锁定现象相关的挑战。坍塌载荷解在适度的计算努力下收敛到下限，其​​中最终的 NS-FE 布局（即在产生高模量变化率的区域上的细网格，同时对那些经历弹性的区域进行粗网格）描述了失败结构线和机制。该方法克服了在不可压缩条件下与应力奇异性和体积锁定现象相关的挑战。坍塌载荷解在适度的计算努力下收敛到下限，其​​中最终的 NS-FE 布局（即在产生高模量变化率的区域上的细网格，同时对那些经历弹性的区域进行粗网格）描述了失败结构线和机制。该方法克服了在不可压缩条件下与应力奇异性和体积锁定现象相关的挑战。坍塌载荷解在适度的计算努力下收敛到下限，其​​中最终的 NS-FE 布局（即在产生高模量变化率的区域上的细网格，同时对那些经历弹性的区域进行粗网格）描述了失败结构线和机制。