Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

The response of nonlinear multi-story structures subjected to earthquake excitation

Abstract: The dynamic responses of a 20-story nonlinear structural frame representative of a modern high rise building are analyzed with the aid of a digital computer. Related analytical studies of continuous systems are carried out. Quantitative information is provided on the importance of a wide range of modes to the various responses of a multi-story structure during an earthquake. The effect of yielding on the response is observed. The magnitude of the structural responses are compared with common measurements of earthquake strength. At the ends of each girder and column of the structural frame are yield hinges which have bilinear bending moment- rotation hysteretic characteristics. Two beam models having such characteristics are studied; one of these models can treat curvilinear hysteretic behavior. Three definitions of ductility factor are discussed, one of which is applicable to both bilinear and curvilinear hysteresis loops. In the computer program, the frame is subjected to the time history of an earthquake accelerogram, the equations of motion are stepwise integrated, and the various structural responses - displacement, bending moments, incurred yielding, etc. - are determined. The agreement between the response parameters resulting from excitation by seven different earthquake ground motions indicates that these response characteristics are determined more by the properties of the structure than by the earthquake. These results throw some light on extreme value statistics of the response of yielding structures subjected to earthquakes. The characteristic patterns observed in the computed responses of the nonlinear structure can be related to analytical studies of linear elastic, shear-type, uniform and tapered continuous cantilever beams.

FGM and Laminated Doubly-Curved and Degenerate Shells Resting on Nonlinear Elastic Foundations: A GDQ Solution for Static Analysis with a Posteriori Stress and Strain Recovery

Abstract: This work focuses on the static analysis of functionally graded (FGM) and laminated doubly-curved shells and panels resting on nonlinear and linear elastic foundations using the Generalized Differential Quadrature (GDQ) method. The First-order Shear Deformation Theory (FSDT) for the aforementioned moderately thick structural elements is considered. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Several types of shell structures such as doubly-curved shells (elliptic and hyperbolic hyperboloids), singly-curved (spherical, cylindrical and conical shells), and degenerate panels (rectangular plates) are considered in this paper. The main contribution of this paper is the application of the differential geometry within GDQ method to solve doubly-curved FGM shells resting on nonlinear elastic foundations. The linear Winkler-Pasternak elastic foundation has been considered as a special case of the nonlinear elastic foundation proposed herein. The discretization of the differential system by means of the GDQ technique leads to a standard nonlinear problem, and the Newton-Raphson scheme is used to obtain the solution. Two different four-parameter power-law distributions are considered for the ceramic volume fraction of each lamina. In order to show the accuracy of this methodology, numerical comparisons between the present formulation and finite element solutions are presented. Very good agreement is observed. Finally, new results are presented to show effects of various parameters of the nonlinear elastic foundation on the behavior of functionally graded and laminated doubly-curved shells and panels.

Soft Tissue Modeling for Surgery Simulation

Abstract: This chapter presents different algorithms for modeling soft tissue deformation in the context of surgery simulation These algorithms make radical simplifications about tissue material property, tissue visco-elasticity and tissue anatomy The chapter describes the principles and the components of a surgical simulator It also presents the process of building a patient-specific hepatic surgery simulator from a set of medical images The different stages of computation leading to the creation of a volumetric tetrahedral mesh from a medical image are especially emphasized Later, it describes the five main hypotheses that are made in the proposed soft tissue models Moreover, the main equations of isotropic and transversally anisotropic linear elasticity in continuum mechanics are also presented The discretization of these equations is presented that are based on finite element modeling The simple linear tetrahedron element is presented that provide closed form expressions of local and global stiffness matrices After describing the types of boundary conditions existing in surgery simulation, the static and dynamic equilibrium equations in their matrix form are derived The chapter introduces a first model of soft tissue; it is based on the off-line inversion of the stiffness matrix and can be computed very efficiently as long as no topology change is required A second soft tissue model allows to perform cutting and tearing but with less efficiency as the previous model A combination of the two previous models, called “hybrid model” is also presented in the chapter It also introduces an extension of the second soft tissue model that implements large displacement elasticity