A displacement-controlled Arc-Length Solution Scheme [dataset].

Tracing load-displacement paths in structural mechanics problems is complicated in the presence of critical points of instability where conventional load- or displacement control fails. To deal with this, arc-length methods have been developed since the 1970s, where control is taken over increments of load at these critical points, to allow full transit of the load-displacement path. However, despite their wide use and incorporation into commercial finite element software, conventional arc-length methods still struggle to cope with non-zero displacement constraints. In this paper we present a new displacement-controlled arc-length method that overcomes these shortcomings through a novel scheme of constraints on displacements and reaction forces. The new method is presented in a variety of serving suggestions, and is validated here on six very challenging problems involving truss and continuum finite elements. Despite this paper's focus on structural mechanics, the new procedure can be applied to any problems that involve nonhomogeneous Dirichlet constraints and challenging equilibrium paths.

在结构力学问题中，当遭遇失稳临界点时，常规荷载控制或位移控制方法会直接失效，此时荷载-位移路径的追踪过程将变得极为复杂。为解决这一技术难题，自20世纪70年代起，弧长法（arc-length method）应运而生：该方法在上述临界点处将控制变量切换为荷载增量，从而实现荷载-位移路径的完整追踪。尽管该方法已得到广泛应用并被集成至商用有限元（finite element）软件中，传统弧长法仍难以妥善处理非零位移约束问题。本文提出一种新型位移控制型弧长法，通过构建位移与反作用力（reaction force）约束的全新框架，克服了传统方法的上述缺陷。本文从多种应用场景对该新型方法进行了系统阐述，并通过6个涵盖桁架与连续体有限元的极具挑战性的算例完成了方法验证。尽管本文聚焦于结构力学领域，但该新型求解流程同样可应用于所有涉及非齐次狄利克雷（Dirichlet）约束与复杂平衡路径的问题。