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Rigidity of formation is an important concept in multi‐agent localization and control problems. The purpose of this paper is to design the control laws to enable the group to asymptotically exhibit the flocking motion while preserving the network rigidity at all times.

The novel approach for designing control laws is derived from a smooth artificial potential function based on an undirected infinitesimally rigid formation which specifies the target formation. Then the potential function is used to specify a gradient control law, under which the original system then becomes an orderly infinitesimally rigid formation.

The strong relationship between the stability of the target formation and the gradient control protocol are utilized to design the control laws which can be proved to make the target formation stable. However, the rigidity matrix is not utilized in the design of control law. Future research will mainly focus on formation control with the relationship of rigidity matrix.

The value of this paper is focused on the control laws design and the control laws could enable the group to asymptotically exhibit the flocking motion while preserving the network rigidity at all times. Also the detailed simulations and experiments are given to prove that the novel approach is available.

The purpose of this paper is to evaluate upholstery deformation by using resonant vibrations of separate zones of the soft part.

By recording the value of resonant frequency at separate points of the plane, it becomes possible to obtain the graph of deformation distribution. It is compared to the graph that demonstrates how rigidity distributes itself in different directions within the upholstery fabric. This enables the evaluation of unevenness of upholstery deformation that is present in different directions.

The provided methodology allows assessing the quality of soft furniture assembly and predicting the exploitation time for its upholstery.

The test results obtained using the original methodology enable the assessment of manufacturing defects existing in various directions (for example, the shape of different parts during the cutting process, the unevenness of seam width and others), as well as the quality of furniture during the production and exploitation process.

The main aim of this work is to evaluate upholstery deformation by using resonant vibrations of separate zones of the soft part.

Provided methodology allows assessing the upholstery deformation of separate parts of soft furniture by exciting resonant vibrations in it.

By recording the value of resonant frequency at separate points of the plane, it becomes possible to obtain the graph of deformation distribution. It is compared to the graph that demonstrates how rigidity distributes itself in different directions within the upholstery fabric. This enables the authors to evaluate the unevenness of upholstery deformation that is present in different directions.

Provided methodology allows assessing the quality of soft furniture assembly and predicting the exploitation time for its upholstery.

The purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one of the sources of errors. In numerical analysis, sometimes handling numerical errors is challenging. However, by applying appropriate algorithms, these errors are manageable and can be reduced. In this study, five novel topological algorithms were proposed in setting up a structural flexibility matrix, and five different examples were used in applying the proposed algorithms. In doing so round-off errors were reduced remarkably.

Five new algorithms were proposed in order to optimize the conditioning of structural matrices. Along with decreasing the size and duration of analyses, minimizing analytical errors is a critical factor in the optimal computer analysis of skeletal structures. Appropriate matrices with a greater number of zeros (sparse), a well structure and a well condition are advantageous for this objective. As a result, a problem of optimization with various goals will be addressed. This study seeks to minimize analytical errors such as rounding errors in skeletal structural flexibility matrixes via the use of more consistent and appropriate mathematical methods. These errors become more pronounced in particular designs with ill-suited flexibility matrixes; structures with varying stiffness are a frequent example of this. Due to the usage of weak elements, the flexibility matrix has a large number of non-diagonal terms, resulting in analytical errors. In numerical analysis, the ill-condition of a matrix may be resolved by moving or substituting rows; this study examined the definition and execution of these modifications prior to creating the flexibility matrix. Simple topological and algebraic features have been mostly utilized in this study to find fundamental cycle bases with particular characteristics. In conclusion, appropriately conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

(1) Five new algorithms were proposed in order to optimize the conditioning of structural flexibility matrices. (2) A JAVA programming language was written for all five algorithms and a friendly GUI software tool is developed to visualize sub-optimal cycle bases. (3) Topological and algebraic features of the structures were utilized in this study.

This is a multi-objective optimization problem which means that sparsity and well conditioning of a matrix cannot be optimized simultaneously. In conclusion, well-conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

Engineers always finding mathematical modeling of real-world problems and make them as simple as possible. In doing so, lots of errors will be created and these errors could cause the mathematical models useless. Applying decent algorithms could make the mathematical model as precise as possible.

Errors in numerical simulations should reduce due to the fact that they are toxic for real-world applications and problems.

This is an original research. This paper proposes five novel topological mathematical algorithms in order to optimize the structural flexibility matrix.

In our previous study, seam pucker simulation baased on mechancial calculation was proposed. Here, the simulation system is extended to consider collision between fabrics and seam pucker simulation of two strips of fabric is carried out. We adopt non‐linear bending rigidity observed in actual fabric tests and obtained results much closer to the real results. With the consideration of collision and the improved treatment of bending rigidity, the following results were obtained. The wave length of wrinkles is more broadly distributed when material puckering is 0.96 or 0.94 compared to the case of 0.98. The wave length increases as the value of bending rigidity does and decreases as Young’s modulus increases. In the case of two strips seam pucker, the distribution of the wave length is wider than the case of the single strip.

Introduces and evaluates a finite‐element computer model which predicts the bending behaviour of fabric in contact with a surface, in order to optimize the design of equipment used for automated processing of apparel. Describes how simulations were executed for all combinations of eight fabrics and three contact surfaces, and presents the experimental results obtained for similar conditions and fabrics. Proves the validity of the computer model by comparing the experimental results with those obtained by simulation. Describes how the computer model could be used to choose the optimum diameter of a fabric feeder picking roller.

Deals with the development of a control system for fabric pick‐and‐place operators based on the Clupicker device. Fabric mechanical properties are analysed for their influence on the motions performed in picking up fabric pieces from a stack. The performance of the picking device on various woven fabrics has been studied. A stepping motor drive to the crank of the Clupicker enabled us to control the normal force applied by the picking wheel on the fabric stack. By controlling the normal force we could make the Clupicker perform well for fabrics with very different properties. A linear regression was found between the minimum normal force required for effective performance of the picker and bending rigidity of the fabric.

THE increasing operational speeds of the modern aeroplane have involved the designer of the aircraft structure in problems which necessitate the experimental determination or calculation, not only of the strength, but also of the stiffnesses of the various major components of the airframe. It has become very apparent that stiffness rather than strength is the determining factor in the design of many aeroplane components.

Particular attention is given to the viscous damping force parameter, stiffness parameter, rigidity parameter, and Brinkman number and plotted their graph for thermal distribution, momentum profile and concentration profile.

In the field of engineering, biologically inspired propulsion systems are getting the utmost importance. Keeping in view their developmental progress, the present study was made. The theoretical analysis explores the effect of heat and mass transfer on non-Newtonian Sisko fluid with slip effects and transverse magnetic field in symmetric compliant channel. Using low Reynolds number, so that the authors neglect inertial forces and for keeping the pressure constant during the flow, channel height is used largely as compared to the ratio of wavelength. The governing equations of fluid flow problem are solved using the perturbation analysis.

Results are considered for thickening, thinning and viscous nature of fluid models. It is found that the velocity distribution profile is boosted for increasing values of the Sisko fluid parameter and porous effect, while thermal profile is reducing for Brinkman number (viscous dissipation effects) for all cases. Moreover, shear-thicken and shear-thinning behavior of non-Newtonian Sisko fluid is also explained through the graphs.

Hear-thicken and shear-thinning behavior of non-Newtonian Sisko fluid is also explained through the graphs.

The purpose of this study is to explore the effect of stitch type and stitch direction on the dynamic drape behavior of the woven fabric.

In this paper, the effectiveness of stitch type and stitch directions on dynamic drape behaviors were investigated. Fabric parts were sewn together with two types of the stitch (lockstitch and overlock stitch) on three different stitch directions (warp, weft and bias (45°)). The static drape coefficients (SDC) of unsewn and sewn fabrics were measured according to the image process method. Dynamic drape coefficients (DDC) of fabrics were also measured using the same method at six different (25, 50, 75, 100, 125, 150 rpms) rotation speeds. Additionally, bending length and bending rigidity were measured using the Cantilever test method.

Experimental results showed that stitch type and stitch directions are effective on the dynamic drape behaviors of the fabric. Overlock stitch resulted in greater DDC than the lock stitch. For both of the stitch type, DDC for the stitch on the warp direction are greater than the stitch on the weft and bias direction for all speeds. In addition, bending length, hence the bending rigidity, are greater for overlock stitch type and always weft direction resulted in greater than the warp and bias direction.

Fabric drape is vital for garment appearance and is gaining popularity with the advancement of virtual technology, enabling virtual visualization of garments. While previous studies have predominantly examined either the static or dynamic drape behavior of individual fabric panels, or solely focused on the static drape behavior of sewn fabrics, this study acknowledges the significance of incorporating the influence of stitch type and direction on dynamic drape behaviors. Considering that fabrics are sewn together to create garments and that DDC provides a more accurate representation of real-time fabric behavior compared to SDC, this research makes a valuable contribution to the existing literature by investigating the impact of stitch type and direction specifically on DDC.