• Journal of the Korean Society for Precision Engineering
• /
• v.15 no.12
• /
• pp.220-225
• /
• 1998

압축성 초탄성 평판의 순수굽힘에 대한 비선형 변형해석의 수학적 정해가 본 논문에 구해져 있다. 이차원 평면 변형도 상태가 해석을 위하여 가정되었으며, 비선형 순수굽힘 변형해석결과는 고전적인 선형 순수굽힘 변형해석결과와 비교되었다. 고전적인 선형굽힘 결과와는 다르게 비선형 순수굽힘 상태에서는 반경방향응력은 영이 아니며 또한 각방향응력도 선형 상태가 아닌 것으로 규명되었다.

• Smart Structures and Systems
• /
• v.18 no.1
• /
• pp.139-154
• /
• 2016

This paper is concerned with the dynamics of hyperelastic solids and structures. We seek for a smart control actuation that produces a desired (prescribed) displacement field in the presence of transient imposed forces. In the literature, this problem is denoted as displacement tracking, or also as shape morphing problem. One talks about shape control, when the displacements to be tracked do vanish. In the present paper, it is assumed that the control actuation is provided by imposed eigenstrains, e.g., by the electric field in piezoelectric actuators, or by thermal actuators, or via analogous physical effects, such as magneto-striction or pre-stress. Structures with a controlled eigenstrain-type actuation belong to the class of smart structures. The action of the eigenstrains can be conveniently characterized by actuation stresses. Our theoretical derivations are performed in the framework of the theory of small incremental dynamic deformations superimposed upon a statically pre-deformed configuration of a hyperelastic solid or structure. We particularly ask for a distribution of incremental actuation stresses, such that the incremental displacements follow exactly a prescribed trajectory field, despite the imposed incremental forces are present. An exact solution of this problem is presented under the assumption that the actuation stresses can be tailored freely and applied everywhere within the body. Extending a Neumann-type solution strategy, it is shown that the actuation stresses due to the distributed control eigenstrains must satisfy certain quasi-static equilibrium conditions, where auxiliary body-forces and auxiliary surface tractions are to be taken into account. The latter auxiliary loading can be directly computed from the imposed forces and from the desired displacement field to be tracked. Hence, despite the problem is a dynamic one, a straightforward computation of proper actuator distributions can be obtained in the framework of quasi-static equilibrium conditions. Necessary conditions for the functioning of this concept are presented. Particularly, it must be required that the intermediate configuration is infinitesimally superstable. Previous results of our group for the case of shape control and displacement tracking in linear elastic structures are included as special cases. The high potential of the solution is demonstrated via Finite Element computations for an irregularly shaped four-corner plate in a state of plain strain.