A Study of Inertia Relief Analysis

Abstract

[Abstract] Inertia relief analysis is regarded as an effective technique for the modeling of unconstrained structural systems. In this paper the principle of inertia relief analysis is first described. Inertia relief capability of commercial finite element packages is discussed. The paper studies the implementation of inertia relief techniques into finite element analysis of a variety of structures. Two types of inertia relief methods of MSC/NASTRAN (conventional inertia relief and automatic inertia relief) are also addressed. The application of inertia relief method in the analysis of unbalanced and balanced structural systems is discussed. I. Introduction The technique of inertia relief has been a well-known approach for the analysis of unsupported systems such as air vehicles in flight, automotives in motion, or satellites in space. The sum of forces and moments are calculated and applied to achieve an equilibrium state in inertia relief analysis. Inertia relief was applied to calculate load redistribution in a helicopter rotor support structure due to flight load imbalances [1]. Inertia relief allowed for the analysis of free structures in space instead of conventional approach of grounding fuselage to landing gears. The finite element model was built with MSC/NASTRAN and the aircraft center of gravity was chosen to be the reference point for inertia relief analysis. Inertia relief method was employed to determine the distribution of nonlinear internal forces in aircrafts by counterbalancing rotor hub loads [2]. Inertia relief was also used to estimate impact loads of a space frame structure composed of welded tubular elements [3]. In order to obtain accurate inertia relief calculation, the periods of applied loads should be much greater than the periods of rigid body modes restrained. Inertia relief was used to balance externally applied forces on a free-flying solar sail [4]. The inertia loads were developed under steady-state rigid body acceleration and the center of mass of the solar sail was selected as the reference point for inertia relief calculation. The finite element model was constructed using ABAQUS and geometric nonlinearity was considered. Moreover, inertia relief method was employed to analyze aeroelasticity of non-rigid airships [5]. Airship nonlinearity was introduced due to large deformations and nonlinear material behavior of envelope membranes. Pagaldipti’s work showed that inertia relief effect had influence on optimal structural designs [6]. The selected constraints for inertia relief calculation eliminated rigid body motions and didn’t generate associated constraint forces while actual structural supports had constraint forces. Thus, the topology optimization was different for the case with inertia relief effects in comparison with the case without inertia relief. The presence of concentrated masses in structural systems with rigid body modes significantly altered load distribution. The implementation of sensitivity correction corresponding to inertia relief load vectors correction is an essential step in optimization procedure. Although inertia relief approach has been widely employed in the simulation of unconstrained aircrafts and space vehicles, the published work has rarely been found. There is still lack of research on inertia relief analysis of diverse types of basic structures and critical structural considerations associated with inertia relief calculation. In this paper, inertia relief method is applied to analyze a variety of structures including spring-mass structures, truss structures, plate structures, and etc. The work is aimed to study various key issues associated with inertia relief analysis, such as conventional inertia relief and automatic inertia relief, the effect of constraints and mass distribution on inertia relief calculation, the accuracy of inertia relief, and critical considerations. Commercial finite element program MSC/NASTRAN is applied to generate numerical results.