The dynamic relaxation form finding method aided with advanced recurrent neural network

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 opti-misation 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.

Test research and computer simulation analysis of construction state during form finding for suspen-dome system

A novel construction method without scaffold work called as assembly-prestressing form finding loop by loop is presented.Based on the theory of finite displacement,the cycle-forward analysis method is presented for its construction calculation,which adopts the finite element method of generalized geometric nonlinearity combined with the application in the real construction process.By means of the combination of the forward analysis according to real construction sequence and the cycle iteration according to the initial strain increment method of cable force adjustment,the influence of the structural geometric nonlinearity and the loss of prestress are taken into account due to prestressing of tendons in turn and so on.If the initial cable forces derived from the method were used for construction,expected cable forces and shape could be assured easily.Simulation analysis achieved real-time tracking and controlling of the construction status.Finally,according to the procedure and parameters in simulating,a model experimental research on the stage of form finding(namely prestressing)was carried out for suspen-dome structure.The feasibility on the assembly-prestressing form finding method loop by loop was testified.The cycle-forward analysis method was established and numerical simulation was performed,and the results show that it was useful for the design and the construction of similar suspen-dome structure.

A FORM FUNCTION METHOD FOR FORM FINDING OF TENSION STRUCTURE

A new form function involving parameters Pi is presented. On the basis of the form function, an initial form of tension structure was Sound by interpolating through the control points on boundary of the structure. The form function can be controlled by changing beta (1) according to the pre-tension and the boundary of the structure. The final form of a tension structure should be an equilibrium system under the pretension. To examine the nature of the initial form, the FEM was used. Many examples show that the initial form gives a very ideal result for equal or unequal pre-tension in two directions of the structure. In general cases, there is little difference between the initial form and the final one.

Kagome Project:Physical and Numerical Modeling Comparison for a Post-formed Elastic Gridshell

An elastic gridshell is an efficient constructive typology for crossing large spans with little material.A flat elastic grid is built before buckling the structure into shape,in active and post-formed bending.The design and structural analysis of such a structure requires a stage of form finding that can mainly be done:(1)With a physical model:either by a suspended net method,or an active bending model;(2)With a numerical model performed by dynamic relaxation.All these solutions have various biases and assumptions that make them reflect more or less the reality.These three methods have been applied by Happold and Liddell[1]during the design of the Frei Otto’s Mannheim Gridshell which has allowed us to compare the results,and to highlight the significant differences between digital and physical models.Based on our own algorithm called ELASTICA[2],our study focuses on:(1)Comparing the results of the ELASTICA’s numerical models to load tests on physical models;(2)The identification of the various factors that can influence the results and explain the observed differences,some of which are then studied;(3)Applying the results to build a full-scale interlaced lattice elastic gridshell based on the Japanese Kagome pattern.