Abstract Static nonlinear analysis of frames and plane stress/strain structures via mathematical programming algorithms has been addressed by many researchers. It has been shown that the method of Dissipated Energy Maximization (DEM) is an efficient algorithm for nonlinear static analysis. This study extends the application of DEM method to the nonlinear dynamic analysis of frames considering bending moment-axial force interaction. The nonlinear static analysis algorithm that is the basis of nonlinear dynamic analysis, and corresponding assumptions including linear-kinematics, lumped-plasticity, piecewise-linear yield function, and the associated flow rule are briefly explained. The dynamic analysis that is carried out by Duhamel integral method is fully formulated. The proposed method traces the nonlinear equilibrium path through a linear mathematical programming process and makes modifications on response of Duhamel's integral to yield the nonlinear response. In addition, the Bauschinger effect (kinematic hardening) is included in the formulations to get more realistic responses. Several examples illustrate the efficiency and accuracy of the proposed method. It has been shown that the method is the most accurate and fastest algorithm compared to conventional methods of nonlinear dynamic analyses.

中文翻译：

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具有各向同性和运动学硬化/软化的框架的非线性动态分析

摘要 许多研究人员已经通过数学规划算法对框架和平面应力/应变结构进行静态非线性分析。已经表明，耗散能量最大化 (DEM) 方法是一种有效的非线性静态分析算法。本研究将 DEM 方法的应用扩展到考虑弯矩-轴力相互作用的框架非线性动力学分析。简要说明作为非线性动力分析基础的非线性静力分析算法，以及相应的假设，包括线性运动学、集中塑性、分段线性屈服函数和相关的流动规则。用 Duhamel 积分法进行的动力分析是完全公式化的。所提出的方法通过线性数学规划过程跟踪非线性平衡路径，并对 Duhamel 积分的响应进行修改以产生非线性响应。此外，配方中包含包辛格效应（运动硬化）以获得更真实的响应。几个例子说明了所提出方法的效率和准确性。与传统的非线性动力分析方法相比，该方法是最准确和最快的算法。几个例子说明了所提出方法的效率和准确性。与传统的非线性动力分析方法相比，该方法是最准确和最快的算法。几个例子说明了所提出方法的效率和准确性。与传统的非线性动力分析方法相比，该方法是最准确和最快的算法。