In this section, we'll cover the following:

• Developing the theoretical foundation for finite element analysis of plate elements.
• Understanding the role of the element stiffness matrix.
• Constructing the constitutive matrix based on material behaviour.
• Deriving the strain–displacement matrix.
• Introducing key concepts such as stress resultants, shape functions, and the Jacobian matrix.
• Applying the Reissner–Mindlin plate theory as the governing mechanical model.

In this section, we establish the theoretical groundwork needed to build a finite element formulation for plate elements. We begin by identifying the element stiffness matrix as the central component of any finite element code, and we explain that its construction depends on two key ingredients: the constitutive matrix and the strain–displacement matrix. To derive these, we adopt the Reissner–Mindlin plate theory, which assumes that plane sections remain straight after deformation but are not necessarily perpendicular to the middle-plane, allowing us to model shear deformation effects.

We then focus on how to construct each of these matrices. We develop the constitutive matrix by defining appropriate stress and strain fields, and we move on to the strain–displacement matrix, which links nodal displacements to element strains. Along the way, we introduce important supporting concepts, including how stresses are converted into stress resultants, how shape functions are used to interpolate field variables, and how the Jacobian matrix facilitates coordinate transformations. Together, these ideas form the essential theoretical basis for everything that follows in the course.

Next up

In the next lecture, we will begin the detailed derivations by defining the displacement and strain fields for a plate element.