A Novel Semi-Analytical Approach for Micro Beams Subjected to Electrostatic Loads and Residual Stress Gradients

Beam structures are widely used in MEMS sensors and actuators. MEMS micro beams are usually curled due to residual stresses and the characteristics of micro beams subjected to both residual stress gradients and electrostatic forces must be investigated for providing accuracy information for designing sensors and actuators. In this work, a novel semi-analytical formulation to address the above needs is proposed. By assuming an admissible deformation shape and utilizing energy method to determine the coefficients of the shape functions, it is possible to find the pull-in characteristics of the curled cantilevers. Detail parametric studies are subsequently performed to quantify the influence of various geometry and processing parameters on the pull-in characteristics of those micro beams. The method and results presented in this work would be very useful for related micro sensors and actuator designs.

A Study of Combined Asymmetric and Cavitated Bifurcations in Neo-Hookean Material Under Symmetric Dead Loading

A study is given of the deformations of an incompressible body composed of a neo-Hookean material subjected to a uniform, spherically symmetric, tensile dead load. It is based on the energy minimization method using a constructed kinematically admissible deformation field. It brings together the pure homogeneous asymmetric deformations explored by Rivlin (1948, 1974) and the spherically symmetric cavitated deformations analyzed by Ball (1982) in one setting, and, in addition, Hallows nonsymmetric cavitated deformations to compete for a minimum. Many solutions are found and their stabilities examined; especially, the stabilities of the aforementioned asymmetric and cavitated solutions are reassessed in this work, which shows that a cavitated deformation which is stable against the virtual displacements in the spherical form may lose its stability against a wider class of virtual displacements involving nonspherical forms.

Plane Deformations of Incompressible Fiber-Reinforced Materials

A continuum theory of finite, plane deformations of composites consisting of materials reinforced by strong fibers is discussed. The composite is assumed to be incompressible, and the fibers are treated as inextensible and continuously distributed. The analysis is not restricted to any particular material behavior such as elasticity, plasticity, or visco-elasticity. Plane deformations are kinematically determinate, in that the deformation can be found by using the constraint conditions and suitable displacement boundary conditions. The reactions to the constraints produce stress equilibrium in any kinematically admissible deformation. The theory admits stress singularities of an unusual kind: a single fiber or normal line can carry a finite load. Simple examples illustrating this and other points of the theory are given.