Page 23 - Mechanics of Microelectromechanical Systems
P. 23
10 Chapter 1
while the second one denotes the axis which is perpendicular to the plane of
the respective strain.
By combining Eqs. (1.25), (1.26) and (1.27), the following equations are
obtained, which are known as Lamé’s equations:
Equations (1.28) contain as unknowns only the three displacements and
In Eqs. (1.28), is Lamé’s constant, which is defined as:
In order for the equation system (1.28) to yield valid solutions, it is
necessary that the compatibility (or Saint Venant’s) equations be complied
with:
Equations (1.24) through (1.30) are the core mathematical model of the
theory of elasticity. More details on this subject can be found in advanced
mechanics of materials textbooks, such as the works of Boresi, Schmidt and
Sidebottom [1], Ugural and Fenster [2] or Cook and Young [3].
Many MEMS components and devices are built as thin structures, and
therefore the corresponding stresses and strains are defined with respect to a
