Computer Methods in Applied Mechanics and Engineering
Unconditionally stable higher-order Newmark methods by sub-stepping procedure
Reference (27)
A unified set of single-step asymptotic annihilation algorithms for structural dynamics
Comput. Methods Appl. Mech. Engrg.
(1994)- et al.
Non-linear oscillations using the finite element technique
Comput. Methods Appl. Mech. Engrg.
(1973) - et al.
Higher-order methods for transient diffusion analysis
Comput. Methods Appl. Mech. Engrg.
(1977) A new algorithm for integration of dynamic systems
Comput. Struct.
(1978)- et al.
Dynamic response of mechanical systems by a weak Hamilton formulation
Comput. Struct.
(1985) - et al.
How to render second-order accurate time stepping algorithms fourth-order accurate while retaining the stability and conservation properties
Comput. Methods Appl. Mech. Engrg.
(1994) The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
(1987)Practical Time-Stepping Schemes
(1990)- et al.
The Finite Element Method
(1991) - et al.
Solving Ordinary Differential Equations I
(1987)
Solving Ordinary Differential Equations II
Application of Hamilton's Law of varying action
AIAA J.
Hamilton, Ritz and elastodynamics
J. Appl. Mech.
Cited by (39)
Directly self-starting higher-order implicit integration algorithms with flexible dissipation control for structural dynamics
2022, Computer Methods in Applied Mechanics and EngineeringAn improved vibration control method of a flexible non-uniform shaped manipulator
2021, Simulation Modelling Practice and TheoryCitation Excerpt :Thus, exact dynamic responses of real systems are almost impossible to obtain. Numerical methods such as Newmark and Runge-Kutta can be used to solve mathematical models of dynamic systems [2–5]. Lazarus et al. [6] presents a finite element electromechanical reduced order model for the nonlinear vibrations of piezoelectric layered beams and using von Kârmân nonlinear strain–displacement relationship.
A fast processing method to perform transient analysis for vibration control
2020, Simulation Modelling Practice and TheoryElectromagnetic wave propagation analysis by an explicit adaptive technique based on connected space-time discretizations
2018, Finite Elements in Analysis and DesignCitation Excerpt :Implicit approaches, on the other hand, are generally unconditionally stable; however, they are usually characterized by higher computational costs. Many procedures can be employed to improve the stability and accuracy of time integration algorithms, such as subcycling techniques [12–14], high-order accurate schemes [15–20], automatic time step control [21–25], etc. As a matter of fact, a lot of research is continuously realized on this field and several time marching techniques are available nowadays for wave propagation analysis [26–39].
An unusual amplitude growth property and its remedy for structure-dependent integration methods
2018, Computer Methods in Applied Mechanics and Engineering