• Composites Research
• /
• 제23권2호
• /
• pp.1-9
• /
• 2010

본 연구는 실린더 내부가 경사가능재료로 코팅된 두꺼운 벽을 가진 실린더의 겉보기 파괴인성치를 해석한 것이다. 실린더는 내부로부터 반경방향의 단일 모서리 균열이 내재되어 있으며, 균열면과 내면에는 내압을 받고 있는 것으로 가정하였다. 소결온도로부터 냉각 결과 균일한 열팽창계수로 인해 실린더에는 비적합 고유스트레인이 생성되었다. 기존의 연구에서 소개된 응력확대계수 평가법에 기초해 겉보기 파괴인성치를 계산하였다. 본 연구에서는 TiC/$Al_{2}O_{3}$ FGM 코팅된 실린더를 사용하였고 겉보기 파괴인성치의 수치적인 결과를 도식화하였다. 재료분포프로파일, 실린더 벽 두께, 적용온도와 코팅두께등이 겉보기 파괴인치에 미치는 영향이 상세히 조사되었으며, 이러한 모든 인자는 실린더의 겉보기 파괴인성치를 조절하는데 중요한 역할을 하는 것으로 밝혀졌다.

• 대한기계학회논문집A
• /
• 제27권5호
• /
• pp.705-712
• /
• 2003

Analysis for the thermal stress distribution in the laminated plates containing a hot-spot(local heating region) is performed. It is assumed that the local heating region induces only mechanical stress by the thermal expansion but effect of the thermal conduction is neglected. The region is regarded equivalent to a homogeneous inclusion expanding in a laminated medium. As an example, Au/YBCO/Al$_2$O$_3$laminate which is often employed for High Temperature Superconducting Fault Current Limiter(HTS FCL) has been analyzed. Effects of heat input, thickness of each layer and the got spot size upon the stress distribution in the hot-spot have been investigated. For a constant heat generation into the hot-spot, as the thickness of the Al$_2$O$_3$substrate increases, the stress in the YBCO layer is peculiarly oscillated, and the curvature of laminate has a maximum at a certain thickness of the Al$_2$O$_3$.

• Smart Structures and Systems
• /
• 제18권1호
• /
• 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.

• Smart Structures and Systems
• /
• 제30권3호
• /
• pp.221-237
• /
• 2022

This paper is concerned with nonlinear modeling and efficient numerical simulation of electrostrictive materials and structures. Two types of such materials are considered: relaxor ferroelectric ceramics and electrostrictive polymers. For ceramics, a geometrically linear formulation is developed, whereas polymers are studied in a geometrically nonlinear regime. In the paper, we focus on constitutive modeling first. For the reversible constitutive response under consideration, we introduce the augmented Helmholtz free energy, which is composed of a purely elastic part, a dielectric part and an augmentation term. For the elastic part, we involve an additive decomposition of the strain tensor into an elastic strain and an electrostrictive eigenstrain, which depends on the polarization of the material. In the geometrically nonlinear case, a corresponding multiplicative decomposition of the deformation gradient tensor replaces the additive strain decomposition used in the geometrically linear formulation. For the dielectric part, we first introduce the internal energy, to which a Legendre transformation is applied to compute the free energy. The augmentation term accounts for the contribution from vacuum to the energy. In our formulation, the augmented free energy depends not only on the strain and the electric field, but also on the polarization and an internal polarization; the latter two are internal variables. With the constitutive framework established, a Finite Element implementation is briefly discussed. We use high-order elements for the discretization of the independent variables, which include also the internal variables and, in case the material is assumed incompressible, the hydrostatic pressure, which is introduced as a Lagrange multiplier. The elements are implemented in the open source code Netgen/NGSolve. Finally, example problems are solved for both, relaxor ferroelectric ceramics and electrostrictive polymers. We focus on thin plate-type structures to show the efficiency of the numerical scheme and its applicability to thin electrostrictive structures.