A LOCAL/GLOBAL SANDWICH HOMOGENIZATION PROCEDURE FOR FINITE ELEMENT SIMULATION

ABSTRACT A new finite element approach to sandwich shells is proposed. It uses existing shell finite elements formulated for homogeneous shells. The "sandwich" nature of the problem is hidden from the main finite element program. Based on several assumptions the proposed homogenization procedure calculates stress increments in a homogeneous fictitious material, called "equivalent", which correspond to the strain increments in the equivalent material points. The stresses in the equivalent material are calculated based on the stress and strain fields in the sandwich layers, which are determined from the incoming strain field for the equivalent material. This procedure is most suitable for including strain softening and other material nonlinear behavior. The approach can be combined with shell elements formulated for homogeneous materials, based on Reissner-Mindlin shell theory or with elements based on a higher order shell theory. It avoids the necessity of formulating special shell elements for sandwich constructions, which in most cases, due to their large number of degrees of freedom, significantly decrease the computational efficiency of the finite element analysis. The sandwich homogenization procedure is combined with a composite micromechanics-based model for woven composites to analyze sandwich shells with woven fabric faces. NOMENCLATURE In the Formulation of the Sandwich Homogenization Procedure INTRODUCTION Due to their numerous advantages sandwich shells are widely used in modern design of all kinds of structures: land, marine and space vehicles, civil and other structures. Many of their properties -geometrical, acoustic, thermal, etc. can be tailored to suit specific design objectives. One of the major advantages of sandwich shells is their very high weight-to-stiffness and weight-to-strength ratio compared to other commonly used structural materials. Along with that, being a combination of several materials with quite different physical properties makes the analysis of sandwich shells difficult and the results produced are often unreliable and far from real behavior. Therefore, approaching the analysis of sandwich shells from theoretical, experimental, computational point of view has been a major challenge for research within the recent decades. Much of the theoretical and computational research carried out in this field utilizes the finite element approach, which has long proved its efficiency and strength in solving problems of different types. Among the recent work in sandwich shell analysis are the studies o

Sandwich Shell Finite Element for Dynamic Explicit Analysis

This work presents the finite element (FE) formulation and implementation of a higher order shear deformable shell element for dynamic explicit analysis of composite and sandwich shells. The formulation is developed using a displacement based third order shear deformation shell theory. Using the differential equilibrium equations and the interlayer requirements, a treatment is developed for the transverse shear, resulting in a continuous, piecewise quartic distribution of the transverse shear stresses through the shell thickness. The FE implementation is cast into a 4-noded quadrilateral shell element with 9 degrees of freedom (DOF) per node. Only C() continuity of the displacement functions is required in the shell plane, which makes the present formulation applicable to the most common 4-noded bilinear isoparametric shell elements. Expressions are developed for the critical time step of the explicit time integration for orthotropic homogeneous and layered shells based on the developed third order formulation. To assess the performance of the present shell element it is implemented in the general nonlinear explicit dynamic FE code DYNA3D. Several problems are solved and results are compared to other theoretical and numerical results. The developed sandwich shell element is much more computationally efficient for modeling sandwich shells than solid elements

Search for supersymmetry in pp collisions at root s=7 TeV in events with a single lepton, jets, and missing transverse momentum

Results are reported from a search for physics beyond the standard model in proton-proton collisions at a center-of-mass energy of 7TeV, focusing on the signature with a single, isolated, high-transverse-momentum lepton (electron or muon), energetic jets, and large missing transverse momentum. The data sample comprises an integrated luminosity of 36 pb-1, recorded by the CMS experiment at the LHC. The search is motivated by models of new physics, including supersymmetry. The observed event yields are consistent with standard model backgrounds predicted using control samples obtained from the data. The characteristics of the event sample are consistent with those expected for the production of tt̄ and W+jets events. The results are interpreted in terms of limits on the parameter space for the constrained minimal supersymmetric extension of the standard model