Towards a Unified Route in Mechanics Based on the Second-Order Real Symmetric Tensor

Abstract

Engineering Mechanics is the bridge and bond between fundamental and specialized knowledge for most engineering students. In the series of textbooks on Engineering Mechanics, students must face too many formulas and equations, which are complicated, tedious and difficult to remember. We are trying to explore the possibility of adopting one second-order real symmetric tensor to include the properties on the tensors of stress, strain, moment of inertia and curvature. The definition and properties of the second-order real symmetric tensor are given, and then they are applied to investigate the rules of stress, strain, moment of inertia and curvature. It can be seen that the formulas for the four tensors can be derived only by displacing the corresponding parameters. This idea casts light on how twice as much can be accomplished with half the effort to learn the whole system of Engineering Mechanics.