Opera-3d Thin Plate Approximation Increases Productivity

Introduction

Many electromagnetic simulations include ferrous geometry with extreme aspect ratios. A good example of this is magnetic signature calculations of naval vessels, where the hull, deck and bulkhead plates are several metres wide but only a few centimetres thick. Opera-3d already has useful features, such as mesh layering and hexahedral / prism elements, that enable these structures to be meshed with high aspect ratio volume elements. But even these tools reach a limit when several plates meet – such as at the junction of a deck and bulkhead with the hull of a ship. Either the junction area becomes considerably over-meshed, increasing throughput time for simulations without improving accuracy, or the model building requires considerable effort to create “bevelled” edges where the plates join.

In Opera version 18R1, a method to improve this has been introduced where the three dimensional volume structure of the plate is replaced with a two dimensional surface representation, accompanied by a Thin plate boundary condition [1]. Hence, any surfaces can meet without introducing extra elements or requiring special modelling.

A ship magnetic signature model

Ship model with some plates removed to show internal structure

Ship model with some plates removed to show internal structure

In this example, the hull, superstructure, decks and bulkheads of a ship have been modelled to determine the vessel’s magnetic signature in the presence of earth’s field. All of these structures are represented using the new boundary condition.

The data requirements for the boundary condition are very simple. A material label is used to specify from which magnetic material the plate is constructed, and the thickness of the plate is given. The boundary condition can use either magnetically linear or non-linear materials.

An athwartships field of -70 A/m, representing the earth’s magnetic field near the equator, has been applied and the model ran as a non-linear simulation. The magnetic flux density in the ship structure can be displayed – here using a cut plane view so that some of the internal values are also visible. Field intensity vectors on a plane one metre above the bottom of the hull are also shown.

Flux density in thin plates and magnetic field intensity vectors

Flux density in thin plates and magnetic field intensity vectors

Although the Thin plate boundary condition is applied to a two dimensional surface, the field on the surface is multivalued. For example, if the magnetic flux enters the plate normally and then largely turns to flow in the plate, the normal component will be discontinuous across the plate.

The same ship has also been simulated with volume elements in the thin plates. The number of equations solved in this model is more than 5 times greater than with the thin sheet model and it takes nearly 10 times longer to solve. The athwartships component of the signature field, computed along a longitudinal line 6 metres below the bottom of the hull along the centre line of the ship, compare very well between the two simulations.

Athwartships component of the magnetic signature field 6m below hull centre line

Athwartships component of the magnetic signature field 6m below hull centre line

Reference

[1] Christopher S. Biddlecombe and Christopher P. Riley, “Improvements to finite element meshing for magnetic signature simulations”, presented at MARELEC 2015 conference, Philadelphia, PA, USA, June 2015