Determination of loads in quasi-symmetric structure with symmetry components

• We use up to four symmetry components for structural analysis of quasi-symmetric structure.
• We examine quasi-symmetric structures based on both principle of general connect and group theory.
• Quasi-symmetric structures are traced back to a symmetric basic and a modifier structure.
• We consider geometrically and mechanically quasi-symmetry.
• Two formulas are given to determine loads in the mentioned structures.

This paper aims to describe the technique to analyse quasi-symmetric structures being subject to a general load. The paper introduces a general way of describing the symmetry properties of the structure, based on group representation theory (rectangular symmetry group C2v) and principle of general connect, and show how to simplify static structural analysis for quasi-symmetric structures with reflection symmetry only.Reflection symmetry is a main feature of the commercial vehicles, thus only this type of symmetry is considered. Naturally, there are a lot of parts in vehicle, where other symmetry types may occur. Two perpendicular symmetry planes are taken into account during examination. For these structures any general load can be split into symmetric and antimetric components, furthermore only four components SS, SA, AS and AA (S – symmetric component, A – antimetric component) are used in the paper during analysis. One part of these structures does not fulfil the geometrical and mechanical “perfect symmetry” requirements; therefore to extend the range of the analysis with using quasi-symmetry is required. This work distinguishes geometrical and mechanical quasi-symmetry, and takes bending moment only into consideration in the presented problems.