In this section, we'll cover:

• How the direct stiffness method and finite element method are built from element-level behavioural models
• Why understanding element behaviour is the first step in structural modelling
• How stress–strain relationships define element behaviour
• The extension from simple uniaxial stress (Young’s modulus) to more complex 3D stress–strain relationships
• The role of elastic theory as a foundation for later applications

In this section, we focus on the fundamental idea that the direct stiffness method and the finite element method are built by modelling behaviour at the element level and then assembling these models into a global representation using matrices. We begin by establishing what it means to model element behaviour, recognising that the first essential step is to understand how individual elements respond to loading before combining them into a complete structural model.

We revisit the familiar uniaxial stress–strain relationship, where stress is proportional to strain through Young’s modulus, and use this as a starting point. From there, we extend the discussion to more complex three-dimensional stress states, where a single constant is no longer sufficient and more advanced constitutive relationships are required. Throughout, we ground our work in fundamental elastic behaviour theory, recognising that these core concepts will underpin much of what we do later in the course.

Next up:

In the next lecture, we begin our study of stress and strain in two dimensions, starting with uniaxial behaviour and extending to biaxial stress states.