Design of Flexible Bodies in Multibody Dynamic Systems Using Equivalent Static Load Method

2008 ◽  
Author(s):  
Byung-Soo Kang ◽  
Yaw-Kang Shyy
Keyword(s):  
Dynamic Systems ◽  
Static Load ◽  
Flexible Bodies ◽  
Equivalent Static Load ◽  
Multibody Dynamic

Modeling Controlled Articulated Flexible Systems Using Assumed Modes: Part II — Numerical Investigation

2001 ◽  
Author(s):  
Theodore G. Mordfin ◽  
Sivakumar S. K. Tadikonda
Keyword(s):  
Multibody Dynamics ◽  
Dynamic Systems ◽  
Flexible Multibody Dynamics ◽  
Companion Paper ◽  
Parameter Variation ◽  
Flexible Bodies ◽  
Simulation Efficiency ◽  
Multibody Dynamic ◽  
Flexible Multibody ◽  
Assumed Mode

Abstract Guidelines are sought for generating component body models for use in controlled, articulated, flexible multibody dynamics system simulations. In support of this effort, exact truth models and linearized large-articulation models are developed in a companion paper. The purpose of the truth models is to aid in evaluating the use of various types of component body assumed modes in the large-articulation models. The assumed mode models are analytically evaluated from the perspectives of both structural dynamics and multibody dynamics. In this paper, component body assumed modes are tested in a linearized large-articulation model. The numerical behavior of the model and its performance in the presence of parameter variation is investigated and explained. The results show that high accuracy, high simulation efficiency, and numerical robustness cannot be simultaneously achieved. However, in many cases, satisfactory levels of all three are achievable. Guidelines are proposed for modeling the flexible bodies in controlled-articulation flexible multibody dynamic systems.

Determination of seismic design forces by equivalent static load method

2003 ◽  
Vol 30 (2) ◽  
pp. 287-307 ◽  
Author(s):  
JagMohan Humar ◽  
Mohamed A Mahgoub
Keyword(s):  
Seismic Design ◽  
Static Load ◽  
Base Shear ◽  
Uniform Hazard Spectra ◽  
Uniform Hazard Spectrum ◽  
Higher Mode Effects ◽  
Mode Effects ◽  
Equivalent Static Load ◽  
Adjustment Factors ◽  
Mode Vibration

In the proposed 2005 edition of the National Building Code of Canada (NBCC), the seismic hazard will be represented by uniform hazard spectra corresponding to a 2% probability of being exceeded in 50 years. The seismic design base shear for use in an equivalent static load method of design will be obtained from the uniform hazard spectrum for the site corresponding to the first mode period of the building. Because this procedure ignores the effect of higher modes, the base shear so derived must be suitably adjusted. A procedure for deriving the base shear adjustment factors for different types of structural systems is described and the adjustment factor values proposed for the 2005 NBCC are presented. The adjusted base shear will be distributed across the height of the building in accordance with the provisions in the current version of the code. Since the code-specified distribution is primarily based on the first mode vibration shape, it leads to an overestimation of the overturning moments, which should therefore be suitably adjusted. Adjustment factors that must be applied to the overturning moments at the base and across the height are derived for different structural shapes, and the empirical values for use in the 2005 NBCC are presented.Key words: uniform hazard spectrum, seismic design base shear, equivalent static load procedure, higher mode effects, base shear adjustment factors, distribution of base shear, overturning moment adjustment factors.

Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems

1996 ◽  
Author(s):  
Radu Serban ◽  
Jeffrey S. Freeman
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Mechanism Analysis ◽  
Algebraic Equations ◽  
First Order ◽  
Direct Differentiation ◽  
Multibody Dynamic ◽  
Standard Techniques

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

scholarly journals Numerical Integration of Multibody Dynamic Systems Involving Nonholonomic Equality Constraints

2021 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Panagiotis Passas ◽  
Elias Paraskevopoulos
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Coupled System ◽  
Weak Form ◽  
Integration Scheme ◽  
Motion Constraints ◽  
Multibody Dynamic ◽  
Time Integration Scheme

Abstract This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton’s second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.

scholarly journals Numerical Simulation of Dynamic Response and Evaluation of Flexural Damage of RC Columns under Horizontal Impact Load

2021 ◽  
Vol 11 (23) ◽  
pp. 11223
Author(s):  
Bin Hu ◽  
Jian Cai ◽  
Jiabin Ye
Keyword(s):  
Static Load ◽  
Impact Load ◽  
Bending Moment ◽  
Internal Force ◽  
Displacement Curve ◽  
Fe Model ◽  
Damage State ◽  
Rc Columns ◽  
Equivalent Static Load ◽  
The Impact

By using the ABAQUS finite element (FE) model, which has been verified by experiments, the deformation and internal force changes of RC columns during the impact process are investigated, and a parametric analysis is conducted under different impact kinetic energies Ek. According to the development path of the bottom bending moment-column top displacement curve under impact, the member is in a slight damage state when the curve rebounds before reaching the peak and in a moderate or severe damage state when the curve exceeds the peak, in which case the specific damage state of the member needs to be determined by examining whether there is a secondary descending stage in the curve. Accordingly, a qualitative method for evaluating the bending failure of RC column members under impact is obtained. In addition, the damage state of RC columns under impact can also be quantitatively evaluated by the ratio of the equivalent static load Feq and the ultimate static load-bearing capacity Fsu.

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