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Abstract How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism. In this study, for investigating tensegrity form‐finding problems, a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network (DR‐NTZNN) form‐finding algorithm is established through analysing the physical properties of tensegrity structures. In addition, the non‐linear constrained optimisation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm. Moreover, the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course, disturbance caused by external force and manufacturing error when constructing a tensegrity structure. Hence, for the purpose of suppressing the noise, a noise tolerant zeroing neural network is presented to solve the search direction, which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability. Besides, the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired. The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology. Eventually, comparing with other existing form‐finding methods, the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm.

How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism. In this study, for investigating tensegrity form‐finding problems, a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network (DR‐NTZNN) form‐finding algorithm is established through analysing the physical properties of tensegrity structures. In addition, the non‐linear constrained optimisation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm. Moreover, the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course, disturbance caused by external force and manufacturing error when constructing a tensegrity structure. Hence, for the purpose of suppressing the noise, a noise tolerant zeroing neural network is presented to solve the search direction, which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability. Besides, the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired. The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology. Eventually, comparing with other existing form‐finding methods, the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm. [ABSTRACT FROM AUTHOR]

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A physical model of the simplest three-dimensional tensegrity unit was built at human scale out of aluminum. Self-stress implementation and static loading tests were performed on this model. At each step, accurate measurements were obtained for all nodal positions and element forces. For the prestressing phase, elongations were imposed, via mechanical devices, in different combinations of elements, called prestress scenarios. Experimental results are compared to the theoretical self-stress state obtained by singular value decomposition of the equilibrium matrix and to numerical simulations using the dynamic relaxation method. It is shown that internal forces follow the same linear trend for all prestress scenarios even if the geometry is significantly impacted. Compressive tests were conducted by hanging masses from the top nodes. It is shown that there exists a unique load-displacement relation that follows the infinitesimal mechanism direction for a finite distance, which depends on the self-stress level. The paper provides a detailed overview of the simplex's structural behavior using both experimental and numerical results while discussing the limitations of the analysis methods explored. Tensegrity structures are composed of compressive elements floating inside a network of prestressed cables. Their unique aesthetics and mechanical properties have always amazed architects, scientists, and engineers. However, the number of tensegrity structures built for civil purposes remains limited. Reasons behind this include a nonintuitive structural behavior with occurrences of insufficient stiffness and lack of robustness as well as a complex construction process that requires introduction of prestressing forces. Consequently, tensegrity structures are often distrusted in favor of other structural systems. Many studies have focused on finding the conditions required for the existence of self-equilibrated prestressing forces that provide stability and stiffness in tensegrity structures. However, few studies have focused on how these prestressing forces can be implemented in a structure, and the discrepancy between theoretical and numerical approaches. For these reasons, a full-scale physical model of a tensegrity module was built and tested with extreme care on the design and experimental testing. This paper presents a comparison of experimental results using two established analysis methods discussing the differences between experimental measurements and numerical models. [ABSTRACT FROM AUTHOR]

Similar to parafoils, ram-air kites are flexible membrane wings inflated by the apparent wind and supported by a bridle line system. A major challenge in estimating the performance of these wings using a computer model is the strong coupling between the airflow around the wing and the deformation of the membrane structure. In this paper, we introduce a staggered coupling scheme combining a structural finite element solver using a dynamic relaxation technique with a potential flow solver. The developed method proved numerically stable for determining the equilibrium shape of the wing under aerodynamic load and is thus suitable for performance measurement and load estimation. The method was validated with flight data provided by SkySails Power. Measured forces on the tether and steering belt of the robotic kite control pod showed good resemblance with the simulation results. As expected for a potential flow solver, the kite's glide ratio was overestimated by 10–15%, and the measured tether elevation angle in a neutral flight scenario matched the simulations within 2 degrees. Based on the obtained results, it can be concluded that the proposed aero-structural model can be used for initial designs of ram-air kites with application to airborne wind energy. [ABSTRACT FROM AUTHOR]

A two-dimensional plate theory, valid for finite elastic deformations with small strains, is derived for incompressible, fiber-reinforced materials. Single-layer plates and two-layer laminates are considered. Numerical simulations illustrate the substantial effect that fiber reinforcement has on wrinkling patterns in the sheet.

Today digital qualification tools are part of many design processes that make them dependent on long and expensive simulations, leading to limited ability in exploring design alternatives. Conventional surrogate modelling techniques depend on the parametric models and come short in addressing radical design changes. Existing data-driven models lack the ability in dealing with the geometrical complexities. Thus, to address the resulting long development lead time problem in the product development processes and to enable parameter-independent surrogate modelling, this paper proposes a method to use images as input for design evaluation. Using a case study on the curtain airbag design process, a database consisting of 60,000 configurations has been created and labelled using a method based on dynamic relaxation instead of finite element methods. The database is made available online for research benchmark purposes. A convolutional neural network with multiple layers is employed to map the input images to the simulation output. It was concluded that the showcased data-driven method could reduce digital testing and qualification time significantly and contribute to real-time analysis in product development. Designers can utilise images of geometrical information to build real-time prediction models with acceptable accuracy in the early conceptual phases for design space exploration purposes. [ABSTRACT FROM AUTHOR]

The structural performance of any building design is often dependent on the geometrical shape, which affects its behavior and stability. Structural consideration and optimization in the conceptual stage of the design process can lead to better solutions and design exploration. In this paper, a design approach for generating and structurally optimizing the geometrical form in the conceptual design phase is presented. The method is applied to a canopy of an ecological island (waste collection center in Rome, Italy). We demonstrate how parametric structural design can facilitate the decision-maker to generate and analyze the optimal design solutions rapidly in the conceptual stage of the design process. Fully parametric models are created in a Rhinoceros3D® environment and interfaced with in-house built algorithms, and Finite Element simulations are performed in DubalRFEM. An ecological island's canopy has been completely redesigned with a Genetic Algorithm and a Dynamic Relaxation Algorithm, resulting in a free-form shape-resistant structure. Finally, the shape-optimized canopy meets various requirements (structural, functional, formal) that improve structural efficiency and design collaboration, such as in the role of the architect and engineer in the design process and in the relationship between the designer and design tools. [ABSTRACT FROM AUTHOR]

Peridynamics (PD) is a new tool, based on the non-local theoryfor modelling fracture mechanics, where particles connected through physical interaction used to represent a domain. By using the PD theory, damage or crack in a material domain can be shown in much practicalrepresentation. This study comparesbetween Prototype Microelastic Brittle (PMB) damage model and a new Quasi-Brittle (QBR) damage model in the framework of the Bond-based Peridynamics (BBPD) in terms of the damage plot.An in-house codeusing Matlab was developedfor BBPD with inclusion of both damage models, andtested for a quasi-static problem with the implementation ofAdaptive Dynamic Relaxation (ADR) methodin the theoryin order to get a faster steady state solutions. This paper is the first attempt to include ADR method in the framework of BBPD forQBR damage model. This paperanalyseda numerical problem with the absence of failure and comparedthe displacement with literature result that usedFinite Element Method (FEM). The obtained numerical results are in good agreement with the result from FEM. The same problemwas used withtheallowanceof the failure to happen for both of the damage models; PMB and QBR, to observe the damage pattern between these two damage models.PMBdamage model produced damage value of roughly twice compared to the damage value from QBRdamage model.It is found that the QBR damage model with ADR under quasi-static loading significantly improves the prediction of the progressive failure process, and managed to model a more realistic damage model with respect to the PMB damage model.

An analysis method to quantify the alternate load paths (ALPs), inspired by the concept of ALP for progressive analysis of buildings, is proposed for steel truss bridges subject to the loss of a critical member. Quantification of ALP in bridges is defined as the spectra of the surrounding members undergoing load redistribution to prevent collapse following the sudden damage to member(s) of a bridge. Two indicators – demand to capacity ratio for linear elastic analysis and strain ratio for nonlinear dynamic analysis – were incorporated into the analysis method and applied to a representative long-span truss bridge. The results of the ALP analysis showed that the three-dimensionality of truss bridges, stemming from the upper and lower braces, sides trusses, floor beam trusses, and the reinforced-concrete deck, played a primary role in protecting the bridge from collapse following the sudden removal of a member(s). [ABSTRACT FROM AUTHOR]

Cable net structures in mesh reflectors are flexible structures, and therefore, a form-finding process to obtain the shape and stiffness is paramount. To achieve a stable shape in equilibrium, the potential energy should be kept in its minimum in the stability analysis. Besides, the force distribution should be as even as possible to ensure the working performance. To satisfy this requirement, we make an improvement on the energy method by using the dynamic relaxation process to minimize the objective energy function. More specifically, dynamic relaxation process is introduced to minimize the potential energy and potential energy function is harnessed as the governor to converge the kinetic process and achieve a stable shape. In this way, the coefficients in objective function are transformed from force densities to forces in the energy method and the dynamic process can mimic the real process of applying prestress. Finally, numerical examples are presented to verify the efficiency of the method. [ABSTRACT FROM AUTHOR]

For tensegrity structures, there are many groups of cables and bars with symmetrical structures or similar internal forces. In this paper, an application of a fuzzy clustering algorithm in the context of form-finding processes for symmetric tensegrity structures is proposed. This algorithm aims to automate grouping, optimize form-finding strategies, and expedite convergence. Point sets are generated through the segmentation of structural components, and Hausdorff distance is used to extract spatial features. Following this, fuzzy clustering automatically groups components with geometric symmetry. The resultant clustering matrix facilitates the refinement of form-finding processes, thus reducing the computational load associated with solving the equilibrium matrix for internal forces within tensegrity structures. By clustering components with analogous internal forces, computational efficiency is enhanced. Additionally, this methodology refines numerical form-finding outcomes based on symmetrical attributes, improving form-finding precision. [ABSTRACT FROM AUTHOR]

Similar to parafoils, ram-air kites are flexible membrane wings inflated by the apparent wind and supported by a bridle line system. A major challenge in estimating the performance of these wings using a computer model is the strong coupling between the airflow around the wing and the deformation of the membrane structure. In this paper, we introduce a staggered coupling scheme combining a structural finite element solver using a dynamic relaxation technique with a potential flow solver. The developed method proved numerically stable for determining the equilibrium shape of the wing under aerodynamic load and is thus suitable for performance measurement and load estimation. The method was validated with flight data provided by SkySails Power. Measured forces on the tether and steering belt of the robotic kite control pod showed good resemblance with the simulation results. As expected for a potential flow solver, the kite’s glide ratio was overestimated by 10–15%, and the measured tether elevation angle in a neutral flight scenario matched the simulations within 2 degrees. Based on the obtained results, it can be concluded that the proposed aero-structural model can be used for initial designs of ram-air kites with application to airborne wind energy.

This paper proposes a stiffness method based structural analysis algorithm for geometrically non-linear structures. In this study, the applied load on the joints has been discretized to a sequence of a few loadings applied. Each loading step produces incremental external nodal displacements, which are added to the corresponding coordinates to get a new geometrical shape of the structure. This process is iteratively repeated until the sum of the loading of all iterations matches the total initial applied loading. The size of the increments affects the technique's accuracy, subsequently affecting the number of iterations. The configuration of non-linear geometrical structures is vital in the work; a slight change of the coordinates makes a considerable variation of nodal displacements. In this paper, three pin-jointed assemblies and a cantilever beam have been examined using the proposed technique; significantly reasonable outcomes emerged, compared to the non-linear approaches, such as Dynamic Relaxation Method (DRM) and Non-linear approach by Kwan. In a numerical sense, the dissimilarity between the results of the conventional Stiffness Matrix (SM) method and the non-linear method is about 228%, while the maximum discrepancy between the proposed approach and the non-linear methods is just above 15%. [ABSTRACT FROM AUTHOR]

The ancient art of origami can be harnessed for the development of adaptive structures, including those at civil-engineering scale. This can be enhanced with biomimetics, the study and development of synthetic mechanisms that mimic the structure or functionality of biological organisms in nature. The origami structure presented in this paper draws inspiration from pill bugs, a species of woodlice that can alter its shape between a flat and a rolled configuration. The panel type origami pill bug structure is modelled as bars, hinges, and active elements for actuation. This paper provides analysis and comparison of a new formulation of the form-finding method called dynamic relaxation for the analytical study with a computer vision algorithm for the experimental study of a 3D-printed model. The objective of this study is to simulate and experimentally validate the quasi-static and dynamic response to characterize the kinematic properties and dynamic behavior of the origami pill bug structure.

The structural performance of any building design is often dependent on the geometrical shape, which affects its behavior and stability. Structural consideration and optimization in the conceptual stage of the design process can lead to better solutions and design exploration. In this paper, a design approach for generating and structurally optimizing the geometrical form in the conceptual design phase is presented. The method is applied to a canopy of an ecological island (waste collection center in Rome, Italy). We demonstrate how parametric structural design can facilitate the decision-maker to generate and analyze the optimal design solutions rapidly in the conceptual stage of the design process. Fully parametric models are created in a Rhinoceros3D® environment and interfaced with in-house built algorithms, and Finite Element simulations are performed in DubalRFEM. An ecological island’s canopy has been completely redesigned with a Genetic Algorithm and a Dynamic Relaxation Algorithm, resulting in a free-form shape-resistant structure. Finally, the shape-optimized canopy meets various requirements (structural, functional, formal) that improve structural efficiency and design collaboration, such as in the role of the architect and engineer in the design process and in the relationship between the designer and design tools.

In this paper, the nonlinear bending of functionally graded carbon nanotube‐reinforced composite (FG‐CNTRC) shell exposed to thermomechanical loading is perused. It is assumed that the composite shell is reinforced in the longitudinal axis and is also made from a polymeric matrix. Mechanical features of the constituents are obtained based on the modified rule of mixture, and they are considered to be temperature dependent (TD). Using the first‐order shear deformation shell theory (FSDT) as well as von Kármán type of geometrical nonlinearity, the equilibrium mathematical relations are derived. Utilizing the dynamic relaxation (DR) procedure combined with the central finite difference method, these mathematical relations are solved in diverse boundary conditions. Finally, roles of carbon nanotube (CNT) distributions, boundary conditions, shell radius, thickness‐to‐radius ratios, volume fraction of CNTs, mechanical loads, thermal gradient, and temperature dependency are examined on the results. From the numerical results, it can be inferred that in the shell with the CC boundary condition, the FG‐O distribution of nanotubes has the maximum deflection, and the lowest deflection belongs to the uniform distribution. However, in the SS boundary condition, the highest and lowest values of deflections are related to V and uniform distributions, respectively. [ABSTRACT FROM AUTHOR]

The load cases of ram air turbine（RAT）system are firstly analyzed aim at the storage scenario and utilization scenario. Then the mathematical models of the constraints under all the load cases are constructed. Based on these mathematical models, the structure optimization model of the ram air turbine system is established by using collaborative optimization method. In this optimization model, the multi-load-cases structure optimization is firstly carried out for the storage scenario and utilization scenario. Meanwhile, the optimized parameters are coordinated with aid of the dynamic relaxation factor. Finally, the integration of relative simulation analysis tools and the optimization are achieved in Isight multidisciplinary design optimization software. The optimization results show that the collaborative optimization method established in this paper can significantly reduce the weight of the ram air turbine system structures. [ABSTRACT FROM AUTHOR]

Branching structure is often used as a supporting structure of the grid shell due to its geometrical and force-transferring features, and the rationality of its shape is very important. The "physical" and "numerical" hanging models can be used for the joint form-finding of the branching structure and free-form grid shell. However, slack elements may exist in the equilibrium model which corresponds to the inefficient members in the form-found branching structure. To solve this problem, a form-finding method of branching structure based on dynamic relaxation is proposed in this study. The proposed method clusters the elements of the branching model and equalizes the axial forces of the elements in the same cluster, in other words, there are no slack elements in the equilibrium branching model. This method overcomes the defect that the equilibrium branching model may have slack elements and needs many manual adjustments during the procedure of determining the rational shape of a branching structure, and effectively prevents the inefficient members existing in the form-found structure. Numerical examples are provided to demonstrate the characteristics of the proposed method and its effectiveness is verified as well. [ABSTRACT FROM AUTHOR]

In some structural systems, such as cable structures, membranes and tensegrity structures, the use of sliding cables allows to reduce the number of elements required to be controlled during tensioning or activation. However, using sliding cables modifies the structural behavior of tensile structures since it alters the distribution of axial forces in structural members. This has been experienced in structures with continuous cables under the assumption of frictionless sliding. However, sliding-induced friction can further alter the behavior of the system. An enhancement of the static analysis of tensile structures with sliding-induced friction is investigated in this paper. In the proposed formulations, the finite-element analysis method and the dynamic relaxation method are combined with a linear complementary approach. Sliding-induced friction is integrated in the formulations through the consideration of the Euler–Eytelwein equation. The importance of considering sliding-induced friction in the static analysis of tensile structures is demonstrated through a series of examples, where it is shown that friction significantly affects the mechanical behavior of the structures. The examples also reveal that the proposed formulations do not affect the computational time of the static analyses. [ABSTRACT FROM AUTHOR]

This paper proposes a stiffness method based structural analysis algorithm for geometrically non-linear structures. In this study, the applied load on the joints has been discretized to a sequence of a few loadings applied. Each loading step produces incremental external nodal displacements, which are added to the corresponding coordinates to get a new geometrical shape of the structure. This process is iteratively repeated until the sum of the loading of all iterations matches the total initial applied loading. The size of the increments affects the technique’s accuracy, subsequently affecting the number of iterations. The configuration of non-linear geometrical structures is vital in the work; a slight change of the coordinates makes a considerable variation of nodal displacements. In this paper, three pin-jointed assemblies and a cantilever beam have been examined using the proposed technique; significantly reasonable outcomes emerged, compared to the non-linear approaches, such as Dynamic Relaxation Method (DRM) and Non-linear approach by Kwan. In a numerical sense, the dissimilarity between the results of the conventional Stiffness Matrix (SM) method and the non-linear method is about 228%, while the maximum discrepancy between the proposed approach and the non-linear methods is just above 15%.

In this article, a new relationship is proposed for the fictitious mass of viscous dynamic relaxation (DR) method. First, incremental equations are derived for DR steps. Using transformed Gershgörin theory, a new relationship is achieved for fictitious mass of viscous DR by formulating modified time step ratio. This procedure presents a new algorithm for the viscous DR method. To evaluate the numerical efficiency of the proposed method, some 2D and 3D truss and frame structures are analyzed with elastic linear and geometrically nonlinear behaviors. Results show that by using the proposed algorithm for fictitious mass, the convergence rate of the viscous DR method is improved so that the proposed algorithm presents the structural response with lower iterations in comparison with other common DR techniques. Communicated by Joerg Fehr. [ABSTRACT FROM AUTHOR]

Background. The aim of this study is to determine the effectiveness of an intensive four-week structured group relaxation- training program (sophrology's dynamic relaxation) on anxiety and depression symptoms in primary care patients with moderate and high anxiety levels. Method. In an experimental study, seventy patients, according to the Hospital Anxiety Depression Scale - Anxiety subscale (HADS-A), cut-off > 8, were randomized to the "well-being and sophrology" or a control program based on physical and mental health recommendations (PMHR). Hospital Anxiety and Depression Scale (HADS) and the State-trait Anxiety Inventory (STAI) ratings were obtained before and after 12 one-hour sessions for 4 consecutive weeks. Results. Sixty-five patients completed the study. The dropout rate was 2.9% (N=1) for the intervention group and 11.4% (N=4) for the control group. Sophrology showed statistically significant improvements in all HADS and STAI subscales for with-in group (p<0.001) and between groups analysis (p=0.001 to 0.046), regardless of gender or age. The pre-post effect sizes (Cohen's d) for anxiety and depression symptoms were large for sophrology (ES=0.84 to 1.36) and small to moderate for the control (ES=0.28 to 0.49). Conclusion: An intensive four-week structured group relaxation-training program "well-being and sophrology" is highly effective in reducing anxiety and depression symptoms in primary care patients with moderate and high anxiety levels. [ABSTRACT FROM AUTHOR]

Flexible rockfall barriers are protection systems against risks of falling rocks. Their complex behaviour is still not well understood and the development of relevant models allowing for quick calculations is a need toward the optimisation of such structures. The key issue is the modelling of the so-called "curtain effect", where the cable net slides along the supporting cables. The present paper proposes hence a model of sliding cable submitted to concentrated forces. It addresses the stability conditions of the centred finite difference scheme, especially in the framework of the Dynamic Relaxation Method where estimates are found for the best possible fictitious masses at nodes. Expressions are derived in the general case, but also for monotonically curved cables and looped cable elements or rings. Elementary problems are shown for validation, before a case study based on experiments conducted during the French National project C2ROP demonstrates the accuracy and the reliability of the proposed methodology. The present study is however limited to quasi-static loadings and therefore needs further developments to be extended to realistic dynamic cases which are discussed in the conclusion. [ABSTRACT FROM AUTHOR]

The steel roof of the BCF‐Arena in Fribourg, Switzerland The following article is dealing with the structural concept and the execution of a steel roof spanning a total area of about 8 500 m2. The structural part is made up of a network of intersecting, underspanned steel beams with variable height, running tangentially around the oval shaped central ring. Their geometrical layout follows the principle of the stress trajectories. In order to optimise tendon geometry, a form‐finding process based on dynamic relaxation was applied. In consideration of the multiple influencing parameters and in the view of the complex geometry, the bearing structure was completely modelled by means of parametrical tools. This enabled a quick study of variants and a very efficient exchange between geometry and computational models. With the help of this tool we were able to meet the very ambitious time schedule. [ABSTRACT FROM AUTHOR]

Pure BST and doped BSTF (with BSTF2: Fe 2 O 3 2 wt % and BSTF4: Fe 2 O 3 4 wt %) ceramics were prepared by solid state reaction. XRD pattern showed the different phases were formed depend on the weight percent of Fe 2 O 3. The crystal size and lattice parameters increased while the lattice strain decreased. The topography of the sintered samples shows increase of the grain size with increasing Fe 2 O 3 ratio and hence enhances the compaction of ceramics. Broadband dielectric spectroscopy was employed to investigate the effect of magnetite nanoparticle on the dielectric properties of the pure BST ceramic. The interfacial polarization and the conductivity contribution reflect the high values of permittivity and its gradual increase as frequency decreases. The two BSTF samples show relaxation peak dynamic originated from presence of immobile species/electrons at low temperatures and defects/vacancies results from the formation of oxygen vacancies originates from the spontaneous change in oxidation states of Fe ions (Fe 3+/Fe2+) at high temperatures. The relaxation rate obeys Arrhenius law at high temperatures in case of BST sample with activation energy 225 kJ/mol. This high value of activation energy at higher temperatures reflects and confirms the slowed down of the dynamics at the interphase and the decoupling nature of the OH-dynamic and the interfacial polarization. Image 1 • The Solid State Technique, SST was used to synthesis pure and Fe 2 O 3 doped BST ceramics. • Different phases were formed depend on the weight percent of Fe 2 O 3. • The crystal size and lattice parameters increased while the lattice strain decreased. • The extremely high permittivity and unusual dynamic behavior at the interphases is due to anisotropy cubic structure. • Pure BST has the highest values of permittivity and lowest values of dielectric loss make it as ideal dielectric material. [ABSTRACT FROM AUTHOR]

Dynamic Relaxation Method (DRM) is an explicit approach for solving the simultaneous systems of equations. In this tactic, the fictitious mass and damping are added to the static governing equations, and an artificial dynamic system is constructed. By using DRM for nonlinear analysis, the structural static equilibrium path is obtained. This outcome is extremely valuable, since it leads to the behavior of structures. Among the finding related to the structural static path are the critical and buckling points for nonlinear structures. In this paper, a new way for calculating the load factor is proposed by setting the external work zero. Mixing the dynamic relaxation scheme with external work technique has not been formulated so far. In all incremental-iterative methods, the load factor increment sign should be determinated by extra calculations. This sign leads to increase or decrease of the load increment. It is worth emphasizing that sign of the load factor increment changes at the load limit points. Therefore, the sign determinations are required in the common work control methods. These disadvantages are eliminated in the proposed algorithm. In fact, the suggested load factor depends only on the Dynamic Relaxation (DR) fictitious parameters. Besides, all DR calculations are performed via vector operation. Moreover, the load factor is calculated only by one formula, and it has the same relation in the all solution processes. In contrast to the arc length techniques, which requires the sign determined, the proposed scheme does not need any sign finding. It is shown that author's technique is quicker than the other dynamic relaxation strategies. To prove the capability and efficiency of the presented scheme, several numerical tests are performed. The results indicate that the suggested approach can trace the complex structural static paths, even in the snap-back and snap-through parts. [ABSTRACT FROM AUTHOR]

In tensegrity structures, there may exist tensile members with very low elongation. This type of tensile member is almost inextensible under the effect of tensile force and cannot effectively utilize length change to calculate axial force, posing challenge in form-finding. In this paper, a modified dynamic relaxation (DR) form-finding method for general tensegrity structures with inextensible tensile members is presented. The method considers the compressive members as rigid bodies and establishes pseudo-dynamic equation that incorporate both forces and torques. The existence of inextensible tensile members constrains on the motion of rigid bodies, the mobility analysis via screw theory can decompose the wrenches acting on the rigid bodies into their degrees of freedom space. Through iterative processes, rigid compressive members movement towards equilibrium poses under the action of unbalanced wrenches within the permissible range of mobilities. Numerical examples demonstrate the effectiveness of the proposed method in form-finding of classic tensegrity, general tensegrity, and clustered tensegrity. • Form-finding method for general tensegrity structures with inextensible tensile members. • Mobility analysis of compressive members in tensegrity structures via screw theory. • Pseudo-dynamic equations considering the compressive members as rigid bodies. • Compressive members move towards equilibrium poses under unbalanced wrenches. • Potential for application in class k tensegrity form-finding. [ABSTRACT FROM AUTHOR]

Branching structure is often used as a supporting structure of the grid shell due to its geometrical and force-transferring features, and the rationality of its shape is very important. The “physical” and “numerical” hanging models can be used for the joint form-finding of the branching structure and free-form grid shell. However, slack elements may exist in the equilibrium model which corresponds to the inefficient members in the form-found branching structure. To solve this problem, a form-finding method of branching structure based on dynamic relaxation is proposed in this study. The proposed method clusters the elements of the branching model and equalizes the axial forces of the elements in the same cluster, in other words, there are no slack elements in the equilibrium branching model. This method overcomes the defect that the equilibrium branching model may have slack elements and needs many manual adjustments during the procedure of determining the rational shape of a branching structure, and effectively prevents the inefficient members existing in the form-found structure. Numerical examples are provided to demonstrate the characteristics of the proposed method and its effectiveness is verified as well.

Membranes are widely applied in the large-span buildings and spatial deployable structures. They are prone to wrinkle under compression due to their small bending stiffness. The wrinkling deformation may affect the surface precision of a membrane structure and its static and dynamic behaviors. Research on the wrinkling behavior of a membrane and its variation with the wrinkle-influencing factors would shed light on the evolution of wrinkles and contribute significantly to the effective control over the wrinkling deformation. In this paper, a rectangular membrane under shear is numerically studied based on the stability theory of plates and shells to explore the wrinkle-influencing factors, such as boundary conditions, pre-stress, thickness and material constants, and their effects on the characteristic parameters of wrinkles. Besides, some of the results are also compared with those derived from the membrane element previously proposed by the authors for a further exploration. Some new and interesting findings are obtained. [ABSTRACT FROM AUTHOR]

Gridshells have been widely used in various public buildings, and many of them are defined over complex free-form surfaces with complex boundaries. This emphasizes the importance of general grid generation and optimization methods in the initial design stage to achieve visually sound and easy-to-manufacture structure. In this paper, a framework is presented to generate uniform, well-shaped and fluency triangular grids for structural design over free-form surfaces, especially those with complex boundaries. The framework employs force-based algorithms and a connectivity-regularization algorithm to optimize grid quality. First, an appropriate distribution of internal points is randomly generated on the surface. Secondly, a bubble-packing method is employed to increase the uniformity of the initial point distribution, and the points are connected using Delaunay-based triangularization to produce an initial grid with rods of balanced length. Thirdly, the grid connectivity is optimized using a range of edge-operations including edge-flip, collapse and split. The optimization process features a grid relaxation objective which includes the degree of the vertices, leading to improved regularity. As a final step, the grid is relaxed to improve fluency using a net-like method. As part of its contribution, this paper, therefore, proposes a metric for fluency, which can be used to quantitatively evaluate the suitability of a given grid for architectural and structural expression. Two case-study examples are presented to demonstrate the effective execution of the grid generation and optimization framework. It is shown that by using the proposed framework, the fluency index of the grid can be improved by up to 157%. • Framework presented for automatic triangular grid generation over free-form surfaces with complex boundaries. • Force-based technique developed to generate and smooth the grid to obtain uniform grids. • Edge-operations including edge-flip, collapse and split employed to optimize connectivity. • New quality index proposed to evaluate the fluency of resulted grids. • Fluency of the grid improved by up to 157% using the framework. [ABSTRACT FROM AUTHOR]

Abstract Molecular dynamics computer simulations are performed to study the structure and dynamic relaxation of the metallic alloys Cu 50 Ag 50 and Cu 50 Zr 50 with and without miscibility gap, respectively. The interactions between the particles are modeled by an effective potential of the modified embedded atom method (MEAM). Cu 50 Zr 50 undercooled liquid shows negative mixing enthalpy; the stronger interaction of heterogeneous atom pairs than that of homogeneous atom pairs, the longer the α-relaxation time and the lower the diffusion coefficient than that of the Cu 50 Ag 50 liquid. Dynamic relaxation is related to the structural heterogeneity: the amount of five-fold symmetry (icosahedron-like) clusters is predominant in Cu 50 Zr 50 melts, which hinders the movement of atoms and increases the dynamic relaxation time. The amount of non-five-fold symmetry (crystal-like) clusters is more pronounced in Cu 50 Ag 50 melts, which leads to shorter dynamic relaxation time and enhanced crystallization of the Cu 50 Ag 50 melt. The quantitative relationship between the five-fold symmetry parameter W and the diffusion coefficient D, as well as the α-relaxation time τ α , is obtained in the two distinct undercooled liquids. The present work provides an understanding of the atomic-scale structure and the dynamic properties in the miscible and immiscible liquid mixtures. Highlights • The miscible and immiscible undercooled liquid mixtures are explored on atomic level. • The structural heterogeneity is explored. • The atomic-scale structure and dynamic properties is provides. • The relationship between W and D as well as τ α is obtained. [ABSTRACT FROM AUTHOR]

Highlights • A MATLAB implementation of 6 DoF elements in a Dynamic Relaxation (DR) algorithm. • Applies a DR algorithm to bending active gridshells suitable for rectangular sections. • Addresses impact of different bracing types. • Addresses impact of different joint models. Abstract Bending active gridshells are structures that involve sophisticated analysis, design and construction processes. Like shells generally, they can achieve large span to thickness ratios. The computational modelling of bending active gridshells will include, in general, both a form-finding stage and a subsequent stage analysing deformations and internal forces under imposed loads. The analysis of bending active gridshells using the dynamic relaxation method is well represented in the literature. This study examines the effects of different joint models and bracing systems on the stiffness of gridshells. The effect of two types of bracing on stiffness is compared. The effects of different joint models are also examined. The computational modelling is carried out by implementing the dynamic relaxation method in MATLAB and validated by reference to closed form benchmark solutions and previously validated finite element models. Significant variations in stiffness are observed for different bracing and joint models. [ABSTRACT FROM AUTHOR]

Active bending is an increasingly popular construction technique that uses elastically bent structural members to form complex curved shapes. The design and analysis of bending-active structures requires an accurate simulation of the bending process, which is often complicated by the occurrence of large displacements. In this article, we propose to combine a previously developed implicit dynamic relaxation method with co-rotational beam elements to obtain a fast and accurate method for form-finding and analysis of bending-active structures. This approach is applied to four test cases. Implicit dynamic relaxation is compared to the classic Newton–Raphson method and conventional dynamic relaxation. The results show that the proposed implicit dynamic relaxation approach can be stabilized intuitively by changing the time step and damping ratio, making it more stable than the classic Newton–Raphson method. Moreover, the proposed approach converges fast compared to the conventional dynamic relaxation: the total computation time is considerably lower, even though the computation time per iteration is higher. Finally, a high accuracy is achieved due to the use of co-rotational beam elements. The combination of high accuracy and low computation time makes this approach well-suited for both form-finding and analysis of bending-active structures. [ABSTRACT FROM AUTHOR]