Geometrically Nonlinear Analysis of Laminated Composite Space Frame Structures Using the Finite Element Method with a Newly Derived Explicit Tangent Stiffness Matrix

Download or read book Geometrically Nonlinear Analysis of Laminated Composite Space Frame Structures Using the Finite Element Method with a Newly Derived Explicit Tangent Stiffness Matrix written by Ardalan Raisi Sofi and published by . This book was released on 2017 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing geometric nonlinearity to structures is an option in almost all available commercial finite element software nowadays, such as ANSYS, ABAQUS, and MSC Nastran. Defining a composite layup given the materials properties of all plies, their fiber orientations and thickness can also be incorporated in all the aforementioned software in addition to SolidWorks Simulation, Autodesk Simulation Mechanical, and Nastran-in-CAD tool integrated into any CAD software including SolidWorks or Autodesk Inventor. Composite laminate is defined on a surface so that 2D plate or shell elements can mesh it. Composite laminates cannot be defined on lines to model beams or 3D frames. Hence, the computational cost of performing static or dynamic analyses on large composite structures, such as trusses or idealized structures with beam elements, becomes very high. The development of a 3D frame element for geometric nonlinear analysis of laminated composite beams is then very effective and efficient due to the expected simplicity and low computational costs. In this thesis, a closed-form expression is derived for the tangent stiffness matrix of a laminated composite beam element undergoing large deformation and rotation. A co-rotational element reference frame is used as the Updated-Lagrangian formulation. Stretching, bending, and torsion have been accounted for laminated fiber reinforce composite structure. The model has been verified in different problems by comparison with the results of Nastran-in-CAD, a tool that enables modeling laminated composites in SolidWorks. In all problems where a comparison was done, the difference in the resulting large deformations is less than 9%, 7.5%, and 8% for displacements along the x1, x2, and x3 directions and 6.5% for rotation about x3 direction. Given the fact that computational time is much less than the case of modeling the laminated composite structure using 2D shell element it is believed that our model provides very fast and efficient tool at least for generating preliminary results for any 3D space frame composite structures. The major advantage of the proposed approach is that the composite structure is modeled using beam elements rather than 2D shell elements with laminated composite material as in the case of using regular finite element (FE) software packages where laminates should be defined over surfaces or shells. The availability of an explicit expression for the tangent stiffness matrix makes the proposed model highly efficient specially when dealing with large composite space frame structures. The tangent stiffness matrix is a matrix that describes the stiffness of a system in response to small changes in configuration. In fact, the tangent stiffness matrix is the stiffness matrix that updating in each iteration of the solution of a nonlinear problem. The saving in computational time could reach 98% compared to conventional FEA software packages. Also, the developed model showed reasonable deformations when loads are applied normal to the plane of the laminate, which is not the case when modeling laminates in regular FEA packages, such as Nastran-in-CAD, Autodesk Simulation Mechanical or SolidWorks Simulation. The developed model will be very useful in modeling flexible composites which have a lot of new applications, such as morphing aerospace structures and flexible robots.