IMPROVING STABILITY IN THE TIME-STEPPING ANALYSIS OF STRUCTURAL NONLINEAR DYNAMICS

A change in the representation of discrete motion equations for nonlinear structural dynamics of two-dimensional bodies is developed. The objective is to write the motion equation in a less nonlinear form. This leads to a significant increase in the range of stability of the time integration process and a reduction in the number of Newton iterations required in the time integration step.

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Combined Viscous and Plastic Deformations in Two-Dimensional Large Strain Finite Element Analysis

Journal of Engineering Materials and Technology ◽

10.1115/1.3225764 ◽

1985 ◽

Vol 107 (1) ◽

pp. 13-18 ◽

Cited By ~ 5

Author(s):

B. V. Kiefer ◽

P. D. Hilton

Keyword(s):

Finite Element ◽

Input Parameter ◽

Time Integration ◽

Strain Increment ◽

Total Strain ◽

Two Dimensional ◽

Elastic Plastic ◽

Time Stepping ◽

Perfectly Plastic ◽

Elastic Perfectly Plastic

Capabilities for the analysis of combined viscous and plastic behavior have been added to an existing finite element computer program for two-dimensional elastic-plastic calculations. This program (PAPSTB) has been formulated for elastic-plastic stress and deformation analyses of two-dimensional and axisymmetric structures. It has the ability to model large strains and large deformations of elastic-perfectly plastic, multi-linear hardening, or power-hardening materials. The program is based on incremental plasticity theory with a von Mises yield criterion. Time dependent behavior has been introduced into the PAPSTB program by adding a viscous strain increment to the elastic and plastic strain increment to form the total strain increment. The viscous calculations presently employ a power-law relationship between the viscous strain rate and the effective stress. The finite element code can be easily modified to handle more complex viscous models. The Newmark method for time integration is used, i.e., an input parameter is included which enables the user to vary the time domain approximation between forward (explicit) and backward (implicit) difference. Automatic time stepping is used to provide for stability in the viscous calculations. It is controlled by an input parameter related to the ratio of the current viscous strain increment to the total strain. The viscoplastic capabilities of the PAPSTB program are verified using the axisymmetric problem of an internally pressurized, thick-walled cylinder. The transient viscoplastic case is analyzed to demonstrate that the elastic-perfectly plastic solution is obtained as a steady-state condition is approached. The influence of varying the time integration parameter for transient viscoplastic calculations is demonstrated. In addition, the effects of time step on solution accuracy are investigated by means of the automatic time stepping algorithm in the program. The approach is then applied to a simple forging problem of cylinder upsetting.

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A Dissipative Momentum-Conserving Time Integration Algorithm for Nonlinear Structural Dynamics

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455421501169 ◽

2021 ◽

pp. 2150116

Author(s):

Salvatore Lopez

Keyword(s):

Angular Momentum ◽

Structural Dynamics ◽

Time Integration ◽

Integration Scheme ◽

Second Phase ◽

Time Step ◽

Integration Algorithm ◽

Nonlinear Structural Dynamics ◽

Nonlinear Structural ◽

Solution Point

A second-order accurate single-step time integration method for nonlinear structural dynamics is developed. The method combines algorithmic dissipation of higher modes and conservation of linear and angular momentum and is composed of two phases. In the first phase, a solution point is computed by a basic integration scheme, the generalized-[Formula: see text] method being adopted due to its higher level of high-frequency dissipation. In the second phase, a correction is hypothesized as a linear combination of the solution in the basic step and the gradient of vector components of the incremental linear and angular momentum. By solving a system composed of six linear equations, the searched for corrected solution in the time step is then provided. The novelty in the presented integration scheme lies in the way of imposing the conservation of linear and angular momentum. In fact, this imposition is carried out as a correction of the computed solution point in the time step and not through an enlarged system of equations of motion. To perform tests on plane and spatial motion of three-dimensional structural models, a small strains — finite rotations corotational formulation is also described.

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