This chapter introduces the concept of Node-Dependent Kinematics (NDK) in Finite Element (FE) modeling of beam structures. In a conventional beam model, the same kinematic assumptions are applied uniformly along the entire beam axis. However, there are situations where certain regions experience localized effects, such as stress concentrations or complex deformations, that necessitate a more sophisticated kinematic description than the other domains of the structure. In these cases, it may be advantageous to refine the kinematic assumptions at specific nodes, while retaining a simpler, lower-order formulation (e.g., a standard bar model) elsewhere. NDK approach enables this flexibility by allowing the kinematic description of each node to vary according to local requirements. When one portion of the beam is subjected to complicated local phenomena, a higher-order kinematic approximation can be employed at the corresponding nodes, capturing the intricate deformation more accurately. Meanwhile, other sections of the beam that do not require such refinement can be modeled using a lower-order kinematic description.

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Stiffness Matrix with Node-Dependent Kinematic

  • Erasmo Carrera,
  • Gerlando Augello,
  • Riccardo Augello

摘要

This chapter introduces the concept of Node-Dependent Kinematics (NDK) in Finite Element (FE) modeling of beam structures. In a conventional beam model, the same kinematic assumptions are applied uniformly along the entire beam axis. However, there are situations where certain regions experience localized effects, such as stress concentrations or complex deformations, that necessitate a more sophisticated kinematic description than the other domains of the structure. In these cases, it may be advantageous to refine the kinematic assumptions at specific nodes, while retaining a simpler, lower-order formulation (e.g., a standard bar model) elsewhere. NDK approach enables this flexibility by allowing the kinematic description of each node to vary according to local requirements. When one portion of the beam is subjected to complicated local phenomena, a higher-order kinematic approximation can be employed at the corresponding nodes, capturing the intricate deformation more accurately. Meanwhile, other sections of the beam that do not require such refinement can be modeled using a lower-order kinematic description.