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The paper presents the design of an adapter to launch several spacecraft. The adapter is a multifaceted composite lattice anisogrid shell. The technique for creating a finite element model of the presented lattice adapter is developed. The influence of structure parameters on the fundamental frequency of oscillations is studied. The results of solv...
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The presented studies of the process of radial-rotational profiling of the rims of the wheels of vehicles are aimed at studying the field of stress-strain. An attempt is made to simulate this dynamic process by a static finite element model. This statement of the problem justifies itself from the viewpoint of the physical nature of the method in a...
Citations
... In this case, the employed discretizations are commonly based on beams or 3D solid finite elements (FEs), see Refs. [25][26][27][28][29]. The mechanical and physical modeling of lattice solids, however, is neither trivial nor computationally inexpensive, for different reasons, namely, the large number of nodes or intersections connecting the structural members, the sizedependent mechanical behaviour of micro-architectured materials and structures, or the possible imperfections resulting from a manufacturing process [30][31][32][33][34]. ...
... [28,51] to evaluate the effect of design parameters on the structural response of cylindrical and conical anisogrid lattice structures, respectively. A numerical procedure, based on the FEM aided by a computer aided design (CAD) modeling and genetic algorithm, was also proposed in [29,52] for the optimization of anisogrid lattice structures or grid-stiffened composite sandwich structures, in accordance with some fixed stiffness and mechanical requirements. ...
The work investigates the vibration behaviour of anisogrid composite lattice shell structures, typically formed by a system of geodesic unidirectional composite ribs. A homogenization approach is here embedded within an Equivalent Single Layer (ESL) formulation for doubly-curved shells, accounting for the geometric contribution of cell patterns. The lattice shells are modelled as anisotropic homogenized continuous structures characterized by effective stiffness parameters. The governing equations of motion are derived using the Higher-order Shear Deformation Theories (HSDTs) of shells, whereas the Generalized Differential Quadrature (GDQ) method is applied to determine the fundamental frequencies with a reduced computational effort. A piecewise field variable assumption is considered for a proper description of zigzag interfacial effects between the lattice core and the external skins. The reliability and efficiency of the proposed numerical strategy is verified by comparison with finite element-based predictions. A systematic analysis aims at studying the effect of different geometric and stiffness parameters, e.g. the number of ribs, their cross-sectional dimensions, orientation and spacing, on the magnitude of the fundamental frequencies for some lattice structural members that could be of great interest for design purposes in the aerospace or automotive engineering practice.
The main aim of this book is to analyze the mathematical
fundamentals and the main features of the Generalized
Differential Quadrature (GDQ) and Generalized Integral
Quadrature (GIQ) techniques. Furthermore, another interesting
aim of the present book is to shown that from the two numerical
techniques mentioned above it is possible to derive two different
approaches such as the Strong and Weak Finite Element
Methods (SFEM and WFEM), that will be used to solve various
structural problems and arbitrarily shaped structures.
A general approach to the Differential Quadrature is
proposed. The weighting coefficients for different basis
functions and grid distributions are determined. Furthermore,
the expressions of the principal approximating polynomials
and grid distributions, available in the literature, are shown.
Besides the classic orthogonal polynomials, a new class of basis
functions, which depend on the radial distance between the
discretization points, is presented. They are known as Radial
Basis Functions (or RBFs). The general expressions for the
derivative evaluation can be utilized in the local form to reduce
the computational cost. From this concept the Local Generalized
Differential Quadrature (LGDQ) method is derived.
The Generalized Integral Quadrature (GIQ) technique can be
used employing several basis functions, without any restriction
on the point distributions for the given definition domain.
To better underline these concepts some classical numerical
integration schemes are reported, such as the trapezoidal rule or
the Simpson method. An alternative approach based on Taylor
series is also illustrated to approximate integrals. This technique
is named as Generalized Taylor-based Integral Quadrature (GTIQ)
method.
The major structural theories for the analysis of the
mechanical behavior of various structures are presented in depth
in the book. In particular, the strong and weak formulations
of the corresponding governing equations are discussed and
illustrated. Generally speaking, two formulations of the same
system of governing equations can be developed, which are
respectively the strong and weak (or variational) formulations.
Once the governing equations that rule a generic structural
problem are obtained, together with the corresponding boundary
conditions, a differential system is written. In particular, the
Strong Formulation (SF) of the governing equations is obtained.
The differentiability requirement, instead, is reduced through
a weighted integral statement if the corresponding Weak
Formulation (WF) of the governing equations is developed. Thus,
an equivalent integral formulation is derived, starting directly
from the previous one. In particular, the formulation in hand is
obtained by introducing a Lagrangian approximation of the
degrees of freedom of the problem.
The need of studying arbitrarily shaped domains or
characterized by mechanical and geometrical discontinuities
leads to the development of new numerical approaches that
divide the structure in finite elements. Then, the strong form or
the weak form of the fundamental equations are solved inside
each element. The fundamental aspects of this technique,
which the author defined respectively Strong Formulation Finite
Element Method (SFEM) and Weak Formulation Finite Element
Method (WFEM), are presented in the book.
