This paper presents and discusses a hybrid-mixed stress (HMS) finite element model for the static and dynamic analysis of 2D reinforced concrete frame structures. It is assumed a physically non-linear behaviour for both concrete and steel. In this model, both the stress and the displacement fields are approximated in the domain of each element. Complete sets of orthonormal Legendre polynomials are used as approximation functions. The use of these functions makes possible the definition of analytical closed form solutions for the computation of all structural operators when a physically linear behaviour is assumed and leads to the development of very effective p- refinement procedures. Due to the nature of the HMS formulation, it is possible to consider the use of both inverse and direct integration schemes at the cross-section level. The time integration procedure uses classical step-by-step techniques, such as Newmark and α-HHT method. The latter is used in order to supress some numerical noise that may occur in the iterative procedure involved in the solution of dynamic non-linear problems. Three different types of damage models, with and without permanent strains, are used to model concrete behaviour. To validate the model, to illustrate its potential and to assess its accuracy and efficiency, several numerical examples are discussed, and comparisons are made with solutions provided by other numerical techniques.

本文介绍并讨论了用于二维钢筋混凝土框架结构静，动态分析的混合混合应力（HMS）有限元模型。假定混凝土和钢都具有物理非线性行为。在该模型中，应力场和位移场都在每个单元的域中近似。正交勒让德多项式的完整集合用作逼近函数。这些功能的使用使假设物理线性行为的所有结构算子计算的解析闭合形式解的定义成为可能，并导致开发出非常有效的p-完善程序。由于HMS公式的性质，可以考虑在横截面级别同时使用反积分和直接积分方案。时间积分过程使用经典的逐步技术，例如Newmark和α-HHT方法。使用后者是为了抑制在解决动态非线性问题所涉及的迭代过程中可能出现的一些数字噪声。具有和不具有永久应变的三种不同类型的损伤模型用于对混凝土行为进行建模。为了验证模型，说明其潜力并评估其准确性和效率，讨论了几个数值示例，并与其他数值技术提供的解决方案进行了比较。