C.F. Liu

Bio: C.F. Liu is an academic researcher from Virginia Tech. The author has contributed to research in topics: Simple shear & Orthotropic material. The author has an hindex of 1, co-authored 1 publications receiving 904 citations.

Theories and Finite Elements for Multilayered Plates and Shells:A Unified compact formulation with numerical assessment and benchmarking

Abstract: This work is a sequel of a previous author’s article: “Theories and Finite Elements for Multilayered. Anisotropic, Composite Plates and Shell”, Archive of Computational Methods in Engineering Vol 9, no 2, 2002; in which a literature overview of available modelings for layered flat and curved structures was given. The two following topics, which were not addressed in the previous work, are detailed in this review: 1. derivation of governing equations and finite element matrices for some of the most relevant plate/shell theories; 2. to present an extensive numerical evaluations of available results, along with assessment and benchmarking. The article content has been divided into four parts. An introduction to this review content is given in Part I. A unified description of several modelings based on displacements and transverse stress assumptions ins given in Part II. The order of the expansion in the thickness directions has been taken as a free parameter. Two-dimensional modelings which include Zig-Zag effects, Interlaminar Continuity as well as Layer-Wise (LW), and Equivalent Single Layer (ESL) description have been addressed. Part III quotes governing equations and FE matrices which have been written in a unified manner by making an extensive use of arrays notations. Governing differential equations of double curved shells and finite element matrices of multilayered plates are considered. Principle of Virtual Displacement (PVD) and Reissner’s Mixed Variational Theorem (RMVT), have been employed as statements to drive variationally consistent conditions, e.g.C 0 -Requirements, on the assumed displacements and stransverse stress fields. The number of the nodes in the element has been taken as a free parameter. As a results both differential governing equations and finite element matrices have been written in terms of a few 3×3 fundamental nuclei which have 9 only terms each. A vast and detailed numerical investigation has been given in Part IV. Performances of available theories and finite elements have been compared by building about 40 tables and 16 figures. More than fifty available theories and finite elements have been compared to those developed in the framework of the unified notation discussed in Parts II and III. Closed form solutions and and finite element results related to bending and vibration of plates and shells have been addressed. Zig-zag effects and interlaminar continuity have been evaluated for a number of problems. Different possibilities to get transverse normal stresses have been compared. LW results have been systematically compared to ESL ones. Detailed evaluations of transverse normal stress effects are given. Exhaustive assessment has been conducted in the Tables 28–39 which compare more than 40 models to evaluate local and global response of layered structures. A final Meyer-Piening problem is used to asses two-dimensional modelings vs local effects description.

Nonlinear Vibrations and Stability of Shells and Plates

Abstract: Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.