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The purpose of the present study is to explore the incomplete substitution of the simplex triangular finite element by either of two models: one evolving out as part of the element flexibility, and the other as part of the element stiffness.

The elastic energy stored in each of the units under stress or strain decides on stiffer and weaker responses. The pertaining Rayleigh quotient in terms of the flexibility matrices allows bounding the distance of the spring cell models to the finite element in dependence of the triangle configuration.

Despite a superiority of the flexibility cell concept observed in computations, the study reveals constellations of shape and stressing of the triangle that favour the stiffness concept. The latter is seen to behave stiffer than its flexibility counterpart and produces results more distant to the finite element in most cases.

The difference between the stiffness and the flexibility approach to spring cells is investigated for triangular elements in dependence of the geometrical configuration under specific conditions of stressing. This suffices to refute an exclusive superiority of the flexibility concept although largely true.

The results of the investigation appear useful in deciding between the spring cell models depending on the case of a spring lattice application.

The flexibility approach to the spring cell is not widely known yet. This cell model deserves a study on performance and comparison to the different, more common stiffness cell model.

An intended numerical analysis of solids and structures by spring cell substitutes in place of finite elements has occasioned considerable research on the subject. This paper aims to expose two alternative concepts evolving out of Argyris’ natural approach to the simplex triangular element. One is based on an approximation of the element flexibility and the other approximates the stiffness with coincidence at the ideal conditions of complete substitution.

Characteristic of the natural formalism is the homogeneous definition of strain and stress along the sides of the triangular element. The associated elastic compliance offers itself for the transition to the spring cell. The diagonal entities are interpreted immediately as springs along the element sides, and the off-diagonal terms account for the completeness of the substitution. In addition to the flexibility concept, the spring cell is deduced alternatively from the element’s natural stiffness. The difference in the flexibility result lies in the calculatory cross-sectional areas of the elastic bar members.

From the natural point of view, the spring cell evolves out of the continuum element to the desired degree of substitution. The simplest configuration of pin-joined bars discards all geometrical and physical cross effects. The approach is attractive because of its transparent simplicity.

The difference between the stiffness and the flexibility approach to spring cells is demonstrated for triangular elements that suit the problems lying in plane stress or plane strain. More general states of stress and strain involve spring cell counterparts of the tetrahedral finite element.

Apart from plane geometries, triangular spring cells are assembled to lattice models of space structures, such as membrane shells and similar.

The natural formalism of simplex finite elements is used for deducing spring cells in two variants and exploring their properties. This is a novel approach to spring cells and an original employment of the natural concept.

The employment of spring cell substitutes for the numerical analysis of solids and structures in place of finite elements has occasioned research on the subject with regard to both, the applicability of existing approaches and the advancement of concepts. This paper aims to explore in the context of linear elasticity the substitution of the simplex tetrahedral element in space and the triangle in the plane by corresponding spring cells deduced on a flexibility basis using the natural formalism.

The natural formalism is characterized by the homogeneous definition of strain and stress along the lines connecting nodes of the simplex tetrahedron and the triangle. The elastic compliance involves quantities along the prospective spring directions and offers itself for the transition to the spring cell. The diagonal entities are interpreted immediately as spring flexibilities, the off-diagonal terms account for the completeness of the substitution. In addition to the isotropic elastic material, the concept is discussed for anisotropic elasticity in the plane.

The natural point of view establishes the spring cell as part of the continuum element. The simplest configuration of pin-joined bars discards all geometrical and physical cross effects. The approach is attracting by its transparent simplicity, revealing deficiencies of the spring cell and identifying directly conditions for the complete substitution of the finite element.

The spring cell counterparts of the tetrahedral- and the triangular finite elements allow employment in problems in three and two dimensions. However, the deficient nature of the approximation requires attention in the design of the discretization lattice such that the conditions of complete finite element substitution are approached as close as possible.

Apart from plane geometries, triangular spring cells have been assembled to lattice models of space structures such as membrane shells and similar. Tetrahedral cells have been used, in modelling plates and shell structures exhibiting bending stiffness.

The natural formalism of simplex finite elements in three and two dimensions is used for defining spring cells on a flexibility basis and exploring their properties. This is a novel approach to spring cells and an original employment of the natural concept in isotropic and anisotropic elasticity.

THE general theorems given in Sections 4 and 6 include, from the fundamental point of view, all that is required for the analysis of redundant structures. However, to facilitate practical calculations it is helpful to develop more explicit methods and formulae. To find these is the purpose of this Section.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Stiffness control of redundant robot arm, aimed at using extra degrees of freedom (DoF) to shape the robot tool center point (TCP) elastomechanical behavior to be consistent with the essential requirements needed for a successful part mating process, i.e., to mimic part supporting mechanism with selective quasi-isotropic compliance (Remote Center of Compliance – RCC), with additional properties of inherent flexibility.

Theoretical analysis and synthesis of the complementary projector for null-space stiffness control of kinematically redundant robot arm. Practical feasibility of the proposed approach was proven by extensive computer simulations and physical experiments, based on commercially available 7 DoF SIA 10 F Yaskawa articulated robot arm, equipped with the open-architecture control system, system for generating excitation force, dedicated sensory system for displacement measurement and a system for real-time acquisition of sensory data.

Simulation experiments demonstrated convergence and stability of the proposed complementary projector. Physical experiments demonstrated that the proposed complementary projector can be implemented on the commercially available anthropomorphic redundant arm upgraded with open-architecture control system and that this projector has the capacity to efficiently affect the task-space TCP stiffness of the robot arm, with a satisfactory degree of consistency with the behavior obtained in the simulation experiments.

A novel complementary projector was synthesized based on the adopted objective function. Practical verification was conducted using computer simulations and physical experiments. For the needs of physical experiments, an adequate open-architecture control system was developed and upgraded through the implementation of the proposed complementary projector and an adequate system for generating excitation and measuring displacement of the robot TCP. Experiments demonstrated that the proposed complementary projector for null-space stiffness control is capable of producing the task-space TCP stiffness, which can satisfy the essential requirements needed for a successful part-mating process, thus allowing the redundant robot arm to mimic the RCC supporting mechanism behavior in a programmable manner.

This study aims to analyse slender thin-walled anisotropic box-beams. Fiber-reinforced laminated composites could play an important role in the design of current and future generations of innovative civil aircrafts and unconventional unmanned configurations. The tailoring characteristics of these composites not only improve the structural performance, and thus reduce the structural weight, but also allow possible material couplings to be made. Static and dynamic aeroelastic stability can be altered by these couplings. It is, therefore, necessary to use an accurate and computationally efficient beam model during the preliminary design phase.

A proper structural beam scheme, which is a modification of a previous first-level approximation scheme, has been adopted. The effect of local laminate stiffness has been investigated to check the possibility of extending the analytical approximation to different structural configurations. The equivalent stiffness has been evaluated for both the case of an isotropic configuration and for simple thin-walled laminated or stiffened sections by introducing classical thin-walled assumptions and the classical beam theory for an equivalent system. Coupling effects have also been included. The equivalent analytical and finite element beam behaviour has been determined and compared to validate the considered analytical stiffness relations that are useful in the preliminary design phase.

The work has analyzed different configurations and highlighted the effect of flexural/torsion couplings and a local stiffness effect on the global behaviour of the structure. Three types of configurations have been considered, namely, a composite wing box configuration, with and without coupling effects; a wing box configuration with sandwich and cellular constructions; and a wing box with stiffened panels in a coupled or an uncoupled configuration. An advanced aluminium experimental test sample has also been described in detail. Good agreement has been found between the theoretical and numerical analyses and the experimental tests, thus confirming the validity of the analytical relations.

The equivalent beam behaviour that has been determined and the stiffness calculation procedure that has been derived could be useful for future dynamic and aeroelastic analyses.

The article presents an original derivation of the sectional characteristics of a thin-walled composite beam and a numerical/experimental validation.

THE primary duties of an aircraft design team are to design an aircraft capable of meeting a certain specification of performance and manoeuvrability with suitable flying qualities, and to ensure that it will be strong enough to withstand any aerodynamic loads it may suffer in flight. It will be found that the aircraft when built is not a rigid structure, but this in itself is not important. We are all familiar with the flexing of an aircraft's wings when struck by a sharp gust of wind in flight, but as long as the wings are strong enough no harm is done. On the contrary, in a passenger aircraft the flexibility of the wings in bending will have a favourable effect, as it will cushion the passengers to some extent from the suddenness of the gust. Flexibility of the structure, however, is not always beneficial and it often introduces new difficulties in the designer's problems. These difficulties arise when the deformation of the aircraft structure introduces additional aerodynamic forces of appreciable magnitude. The additional forces will themselves cause deformation of the structure which may introduce still further aerodynamic forces, and so on. It is interactions of this type between elastic and aerodynamic forces which lead to the oscillatory phenomenon of flutter, and to the non‐oscillatory phenomena of divergence and reversal of control. The study of these three aero‐elastic problems becomes more important as aircraft speeds increase, because increase of design speeds leads to more slender aircraft with thinner wings, and therefore to relatively greater flexibility of the structure. The dangers, in fact, are such that the designers of a modern high‐performance aircraft have to spend considerable effort on the prediction of aero‐elastic effects in order that suitable safeguards can be included in the design. By far the greatest part of this effort is spent on flutter, which will be discussed in Parts II, III and IV of this series, but any of the three problems may force the designers to increase the structural stiffness of parts of the aircraft. The wing skin thickness on a modern aircraft, for example, is nearly always designed by consideration either of aileron reversal or wing flutter. Divergence is usually less important but as it is the simplest of the three phenomena to treat analytically, we shall study it first.

The interest in the ability to detect damage at the earliest possible stage is pervasive throughout the civil engineering over the last two decades. In general, the experimental techniques for damage detection are expensive and require that the vicinity of the damage is known and readily accessible; therefore several methods intend to detect damage based on numerical model and by means of minimum experimental data about dynamic properties or response of damaged structures. The paper aims to discuss these issues.

In this paper, the damage detection problem is formulated as an optimization problem such as to obtain the minimum difference between the numerical and experimental variables, and then a modified ant colony optimization (ACO) algorithm is proposed for solving this optimization problem. In the proposed algorithm, the structural damage is detected by using dynamically measured flexibility matrix, since the flexibility matrix of the structure can be estimated from only the first few modes. The continuous version of ACO is employed as a probabilistic technique for solving this computational problem.

Compared to classical methods, one of the main strengths of this meta-heuristic method is the generally better robustness in achieving global optimum. The efficiency of the proposed algorithm is illustrated by numerical examples. The proposed method enables the deduction of the extent and location of structural damage, while using short computational time and resulting good accuracy.

Finding accurate results by means of minimum experimental data, while using short computational time is the final goal of all researches in the structural damage detection methods. In this paper, it gains by applying flexibility matrix in the definition of objective function, and also via using continuous ant colony algorithm as a powerful meta-heuristic techniques in the constrained nonlinear optimization problem.

This paper computationally estimates the constitutive relationships of composite materials reinforced by single walled carbon nanotubes (SWNT).

A multiscale analysis is considered. At the nanoscale level, molecular dynamics (MD) are used to predict the stiffness for an equivalent beam. A BEM solver for the elasticity problems is extended to allow the presence of inclusions and hence is used to model a RVE for the composite matrix with the equivalent nanotube beams. A genetic algorithm (GA) is developed to generate an initial population of anisotropic materials based on FEM. The GA evolves the population of properties of anisotropic materials till a material is found whose mechanical response is the same as that of the nanocomposite.

The overall process is suitable for the constitutive relationships estimation according to the verification process outlined.

The present work is limited to 2D linear problems. However, extending it to 3D non‐linear applications is straight forward.

The present technique could be used to estimate properties of NCT composites, hence practical applications such as aeroplane structures or turbine blades could be analysed using commercial finite element software. The present methodology could be used to estimate non‐mechanical properties such as the thermal and electric properties.

The present computational technique has never been presented in the literature.