Inertia-based load balancing

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

ProductsAbaqus/Standard

Features tested

The verification problems contained in this section cover the common use cases for inertia relief in Abaqus/Standard. Relatively simple configurations have been selected to demonstrate how inertia-based load balancing can be used in static and direct-integration implicit dynamic steps.

Automobile suspension component

The structure analyzed in this problem is an automobile suspension component modeled with beam elements. The model is loaded with concentrated forces and moments at all free nodes. Inertia relief is used to find out if the applied loads are in equilibrium.

Static step

Elements tested

B31

Problem description

Model:

The model consists of B31 elements with a circular cross-section configured to model the automobile A-arm.

Material:

Density = 7800 kg/m3, Young's modulus = 200× 109N/ m2, Poisson's ratio = 0.3.

Boundary conditions:

The model is fully constrained at node 3.

Loading:

The model is loaded with concentrated forces and moments at all free nodes

Results and discussion

The analysis provides rigid body accelerations and corresponding inertia relief loads that balance the out-of-balance applied loads. The problem demonstrates how inertia relief can be used in place of a more expensive dynamic analysis to obtain constant rigid body accelerations.

Input files

irl_axle_b31.inp

Inertia relief for automobile suspension component.

Assembly loading and free body motion of a rocket under thrust

The problem models assembly loading and liftoff of a rocket. The inertia relief step provides the free body acceleration and static stresses due to the rocket thrust.

Static step

Elements tested

CAX4

Problem description

Model:

The model consists of CAX4 elements with assembly loading modeled as a pre-tension bolt load. The thermal loading during lift-off and rocket thrust are modeled through internal and external pressures.

Material:

  • Rocket: Density = 7800 kg/m3, Young's modulus = 200× 109 N/ m2, Poisson's ratio = 0.3.

  • Engine: Density = 7000 kg/m3, Young's modulus = 700× 107 N/ m2, yield stress =380× 106 N/ m2 .

Boundary conditions:

The model is fixed at node 5 and has roller support at nodes 6, 7, and 8.

Loading:

  • Step 1: A pre-tension section bolt loading is applied to simulate assembly loads, and a gravity load is applied for weight. These loads are propagated to the second and third steps.

  • Step 2: Pressure loading to simulate thrust and thermal loads.

  • Step 3: Inertia relief load.

Results and discussion

The results demonstrate how the inertia relief can be used for different types of loads and materials in a geometrically nonlinear analysis.

Stability analysis of a submerged structure (submarine)

This problem demonstrates how inertia relief can be used to establish initial static equilibrium when the external loads are not fully known.

Direct-integration implicit dynamic step

Elements tested

CPE4

Problem description

Model:

The model consists of a longitudinal section of a submarine under gravity load and hydrostatic pressure at 52.5 m below sea level.

Material:

Density = 7800 kg/m3, Young's modulus = 200× 109 N/ m2 , Poisson's ratio = 0.3, yield stress at 0 plastic strain = 380× 106 N/ m2, yield stress at 0.35 plastic strain = 580× 106 N/ m2.

Boundary conditions:

No boundary conditions are applied in this model.

Loading:

A transient dynamic procedure is used with the gravity load and hydrostatic pressure applied instantaneously, and a pressure load simulating shock-wave loading is ramped over the step.

Results and discussion

The results show that inertia relief can provide the unknown inertia forces that keep a submarine in equilibrium under static preload.

Inertia relief with multiple load cases

This problem demonstrates how inertia relief can be used with multiple load cases.

Static step

Elements tested

CPE4

Problem description

Model:

This problem consists of an airplane modeled as a free body with no boundary conditions. Multiple load cases are used to model various loading scenarios.

Material:

Density = 7800 kg/m3, Young's modulus = 200× 109 N/ m2, Poisson's ratio = 0.3.

Boundary conditions:

No boundary conditions are applied in the model.

Loading:

  • Step 1: Multiple load cases are used to model various combinations of pressure loading with inertia relief loading.

Results and discussion

The results show that inertia relief can be used with multiple load cases to analyze various loading scenarios efficiently.

Inertia relief of a model with substructures

This problem demonstrates how inertia relief can be used with substructures in a geometrically linear analysis.

Static step

Elements tested

T2D2

Problem description

Model:

The problem consist of an overhead hoist crane modeled using substructures. Each member is 1 m in length and 5 mm in diameter.

Material:

Density = 7800 kg/m3, Young's modulus = 200 × 109 N/ m2, Poisson's ratio = 0.3.

Boundary conditions:

The hoist is a simple pin-joined frame work that is constrained at the left end and mounted on rollers at the right end. The members can rotate freely at the joints.

Loading:

  • Step 1: A concentrated load is applied at node 102.

Results and discussion

This analysis shows that inertia relief can be used with substructures.