Dynamic Simulation of Reeving Systems With the Extension of the Modal Approach in the Axial Direction

In this work, the simulation of reeving systems has been studied by including axial modes using the Arbitrary Lagrangian-Eulerian (ALE) description. The reeving system is considered as a deformable multibody system in which the rigid bodies are connected by the elastic wire ropes through sheaves and reels. A set of absolute nodal coordinates and modal coordinates is employed to describe the motion and deformation in the axial direction. This new method allows the analysis of elements with non-constant axial strain along its length. In addition, modal coordinates are employed to describe the dynamic motion in the transverse direction. The non-constant axial displacement within the wire rope is computed in terms of the absolute position coordinates, longitudinal material coordinates, and modal deformation coordinates. To derive the governing equations of motion, Lagrange’s equation is employed. The formulation is validated for a simple pendulumlike motion actuated by an initial velocity. The simulation results are provided to trace the movements of the payload. It can be seen that by adding modal coordinates, the axial force within the element changes. Moreover, the effects of modal coordinates in the axial direction are presented for a different number of nodes, and the resulting axial forces are compared with reference solution.

Axis formation in annual killifish: Nodal coordinates morphogenesis in absence of Huluwa prepatterning

Axis formation in fish and amphibians is initiated by a prepattern of maternal gene products in the blastula. The embryogenesis of annual killifish challenges prepatterning models because blastomeres disperse and then re-aggregate to form the germ layers and body axes. This dispersion-aggregation process prompts the question how axis determinants such as Huluwa and germ layer inducers such as Nodal function in annual killifish. Here we show in Nothobranchius furzeri that huluwa, the factor thought to break symmetry by stabilizing β-catenin, is a non-functional pseudogene. Nuclear β-catenin is not selectively stabilized on one side of the blastula but accumulates in cells forming the incipient aggregate. Inhibition of Nodal signaling blocks aggregation and disrupts coordinated cell migration, establishing a novel role for this signaling pathway. These results reveal a surprising departure from classic mechanisms of axis formation: canonical Huluwa-mediated prepatterning is dispensable and Nodal coordinates morphogenesis.

A novel method for determining the feasible integral self-stress states for tensegrity structures

The form-finding analysis is a crucial step for determining the stable self-equilibrated states for tensegrity structures, in the absence of external loads. This form-finding problem leads to the evaluation of both the self-stress in the elements and the shape of the tensegrity structure. This paper presents a novel method for determining feasible integral self-stress states for tensegrity structures, that is self-equilibrated states consistent with the unilateral behaviour of the elements, struts in compression and cables in tension, and with the symmetry properties of the structure. In particular, once defined the connectivity between the elements and the nodal coordinates, the feasible self-stress states are determined by suitably investigating the Distributed Static Indeterminacy (DSI). The proposed method allows for obtaining feasible integral self-stress solutions by a unique Singular Value Decomposition (SVD) of the equilibrium matrix, whereas other approaches in the literature require two SVD. Moreover, the proposed approach allows for effectively determining the Force Denstiy matrix, whose properties are strictly related to the super-stability of the tensegrity structures. Three tensegrity structures were studied in order to assess and discuss the efficiency and accuracy of the proposed innovative method.

Investigation on design methods for cable mesh configuration of deployable space antenna reflector

Mesh reflectors are always a preferable option for large size deployable antenna reflector over solid surface reflectors due to their flexibility of adjustment in minimum possible space and ability to get deployed to full configuration in space. Maintaining surface properties and accuracy are two important requirements in the design of the mesh reflector for the performance of cable network antenna reflectors. The present work considers the various design approaches for cable mesh configuration of space deployable antenna reflectors. The equal force density shape forming criteria such is applied for obtaining the desired parabolic curvature of the mesh configuration. The ring structure for the deployable mechanism is considered as rigid linkages for designing mesh configuration. A generalized numbering scheme for nodes and cable mesh link is formulated for carrying forward various shapes forming criteria which help in making an algorithm. The algorithm for a better understanding of these methods is developed using MATLAB with nodal coordinates and its connection. Mesh configuration is developed with a different number of divisions. A study is also carried out for finding the required number of divisions for a highly accurate parabolic profile for a particular band frequency. A demonstration model is developed and a comparison of the coordinates of the prototype is made with those arrived at using the model.

Form-Finding of Spine Inspired Biotensegrity Model

This paper presents a study on form-finding of four-stage class one self-equilibrated spine biotensegrity models. Advantageous features such as slenderness and natural curvature of the human spine, as well as the stabilizing network that consists of the spinal column and muscles, were modeled and incorporated in the mathematical formulation of the spine biotensegrity models. Form-finding analysis, which involved determination of independent self-equilibrium stress modes using generalized inverse and their linear combination, was carried out. Form-finding strategy for searching the self-equilibrated models was studied through two approaches: application of various combinations of (1) twist angles and (2) nodal coordinates. A total of three configurations of the spine biotensegrity models with different sizes of triangular cell were successfully established for the first time in this study. All members in the spine biotensegrity models satisfied the assumption of linear elastic material behavior. With the established spine biotensegrity model, the advantageous characteristics of flexibility and versatility of movement can be further studied for potential application in deployable structures and flexible arm in the robotic industry.

Grid patterns optimization for single-layer latticed domes

In previous studies on optimized single-layer latticed domes, the inner space and external shape of the optimized dome is different from those of the initial dome. This difference may result in loss of structural functionality and aesthetics intended by the designers, making it difficult to separately evaluate the mechanical properties of the grid patterns and shape of the surface. In this study, 64 types of single-layer latticed domes having different geometric properties are optimized to obtain mechanically effective grid patterns. Six types of objective functions are employed. The nodal coordinates of the domes serve as the design variables under geometrical constraints, where the nodes of the domes can be shifted on the surface area. The geometric and mechanical properties of the optimized grid patterns are evaluated quantitatively against the objective functions. Moreover, interactions between the geometric and mechanical properties are investigated. The results show that the optimized grid pattern has superior mechanical properties and geometric imperfection sensitivity. This optimization scheme can be applied for designing mechanically effective grid patterns for single-layer latticed domes.

Development of a new empirical formula for prediction of triple point path

This paper develops a new empirical formula for the prediction of the triple point path in irregular shock reflection cases. Numerical simulations using a two-dimensional axisymmetric multi-material arbitrary Lagrangian–Eulerian formulation are employed to obtain the data of fluid density. Using the data of fluid density and nodal coordinates, the gradients of fluid density are determined and then used to generate numerical schlieren images. Based on these images, the triple point paths are derived and compared with the models of the Unified Facilities Criteria (UFC) and Natural Resources Defense Council (NRDC) as well as two models from the open literature. It is found that the numerically derived triple point paths are in good agreement with those predicted by a recently published model in the open literature for the typical ground range of shock wave propagation of up to 6 m. Considering the whole distance range, it is found that the agreement of different models of the triple point path with the numerical ones depends on the considered blast scenario, i.e., the scaled charge height. For small-scaled charge heights, the model of the UFC and the recently published model in the open literature are in better agreement with the numerical results than the other two models, whereas the NRDC model has the best agreement with the numerical results for large-scaled charge heights. Based on the numerical results, a new empirical formula is proposed for the prediction of the triple point path, which is valid for a wide range of the scaled charge heights from 0.5 to 3.5 m/kg1/3 and scaled ground distances up to 15 m/kg1/3.

Buckling analysis of beam structure with absolute nodal coordinate formulation

Absolute nodal coordinate formulation (ANCF) was applied to the buckling analysis. A delicate analysis scheme based on dichotomy method was proposed to solve the buckling problem with beam elements whose tangent stiffness matrix is a highly nonlinear function of nodal coordinates. Three existing planar beam elements are employed to show the application. The accuracy and capability of the ANCF beam for buckling analysis was validated with benchmark cases. Additionally, the influence of the shear effect on the buckling load is thoroughly investigated by comparing the solutions associated with different shear stiffness and slenderness.

Simulation of Dynamics During Deployment of Foldable Origami Structures

Foldable origami-based structures are a type of deployable structures that are increasingly applied in the space and building industries. When folded, the small size of such structures facilitates transportation and storage. Meanwhile, the properties of their larger deployed state may be of interest to different applications. A stable working condition is established by locking the structure in its deployed state, as in the process of deployment, the driving forces may generate a dynamic effect, thus leading to instability of the system. Hence, the study of dynamic characteristics of such structures, including trajectory, duration, velocity, and acceleration is of paramount importance. In this paper, based on the general dynamic equation and Lagrange’s equations of the first kind, the finite element method is adopted to investigate the dynamic deployment of foldable plate structures in terms of the generalized nodal coordinates. The proposed geometric description of a quadrilateral plate element is based on a folding plate composed of refined triangular elements, which are used to approximate the real shells in the structure. Subsequently, a MATLAB framework is developed on the basis of the element using the Newmark integration and the Newton–Raphson iteration method to simulate the deployment process of the structure. Comparisons between MATLAB results and ADAMS results verify the reliability of the framework in analyzing the dynamic deployment of the foldable origami-based structures with sufficient accuracy.