Morphology And Stiffness Characteristics Of Symmetric Prestressed Cable-Strut Structures

Prestressed cable-strut structures have attracted much attention because of their novel configurations,excellent performance,light weight and high efficiency.These structures have become a hot spot in the field of space structures,showing great vitality and broad application prospects.Compared with traditional rigid structures,these prestressed cablestrut structures mainly depend on initial prestresses to obtain or improve their overall stiffness.The strong coupling between its configuration and internal force makes the design analysis more complicated.Therefore,research and analysis of the morphological and stiffness characteristics of this type of structures is the foundation of popularizing novel prestressed cable-strut structures to practical engineering.The main research contents include:On the basis of previous research work,this thesis has carried out an intensive research and investigation towards the morphology and stiffness characteristics of symmetric prestressed cable-strut structures.Analytic and numerical means including group theory,matrix analysis,force density method,finite element method,particle swarm optimization algorithm and so on have been adopted in the researches.Based on group theory,an analytical form-finding method for symmetric cable-strut structures is proposed.The form finding objects can be divided into two types: tensegrity structure and restrained cablestrut system.Based on irreducible representation and the transformation relationship between nodes under symmetry operations,the symmetry subspaces of the structure are established.The key block matrix in the symmetry-adapted force density matrix is obtained according to the irreducible representation associated with the rigid-body translation.Thus,analytic expressions for the force densities of the members can be obtained.The proposed method avoids repeated analysis on the high-dimensional integral force density matrices.The particle swarm optimization(i.e.,PSO)algorithm is introduced to establish the optimal model of the integral feasible prestress of a general cable-strut structure.The fitness function was established by using the weight coefficient method,and the multi-objective optimization problem was converted into single objective optimization problem.The integral feasible prestress is obtained from the independent self-stress modes of the structure.The results of the PSO algorithm are compared with the conventional fminsearch algorithm.It is proved that the proposed optimization algorithm is suitable for the solution of the integral feasible prestress of cable-strut structures with multi self stress modes.The first sub-matrix of the symmetry-adapted equilibrium matrix is associated with specific physical meaning.It is deduced that the existence of zero space in the first sub-matrix of of the symmetry-adapted equilibrium matrix is a necessary condition for the balance of the structure.The PSO algorithm is used to establish a mathematical model for solving the integral feasible prestress from the integral prestress modes.Combined with force density method,a numerical form-finding method is proposed for symmetric prestressed cable-strut structures with multiple integral pretress modes.The consistency of the form-finding results with analytical solutions and the results of the existing literatures proves that the proposed method is suitable for both two-dimensional and three-dimensional structures.The method provides a new idea for the preliminary design and morpholigy optimization of novel cable strut structures.Based on the generalized inverse theory,the zero-stress state of the structure is obtained by releasing the internal force of the active member of a prestressed cable-strut structure.The inverse matrix of the harmonious matrix is obtained by the Moore-Penrose generalized inverse,then the relationship between the axial deformation and the nodal displacement is established.The target of the iteration is that the unbalanced force of the node is zero,and the structural configuration and the length of elements under zero stress are obtained simultaneously.It solves the problem of stress "drift" in the finite element modeling of prestressed cable-strut structures.Moreover,it provides a reference for structural configuration before the construction of prestressed cable-strut structures.Based on group theory and the transformation matrix for the fully symmetry subspace,the structural unbalanced force and nodal displacement are converted into low dimensional symmetry-adapted unbalanced force vectors and nodal displacement vectors.The load-displacement relationship is established using the first sub-matrix of the symmetry-adapted tangent stiffness matrix,and the form-finding analysis is carried out.The absolute value of the minimum eigenvalue of the first sub-matrix of the symmetry-adapted tangent stiffness matrix is used to modify its own nonpositive definiteness,and the iteration step is adjusted according to the principle of minimum potential energy.Numerical examples show that the proposed form finding method can preserve the symmetry of the structure in the iterative process and has good convergence.Using the correspondence between the sub-matrix of the symmetry-adapted stiffness matrix and the symmetry subspace,the stiffness matrix corresponding to each symmetry subspace is separated.The eigenvalue analysis method is used to explore the stiffness characteristics within each symmetry subspace and the stiffness characteristics of each symmetry subspace.The contribution of different types of elements to the structural stiffness was investigated.The element type and the single element with the greatest contribution to stiffness are analyzed,providing reference for the importance judgement of the element and the optimization of the section size.The effects of different prestress levels on the tangent stiffness,elastic stiffness and geometric stiffness of the structures were analyzed.The result shows that the geometrical stiffness increases with the increase of the prestress level of the structure,but the increase of the geometrical stiffness is much smaller than that of the prestress level,while prestress level has little effect on elastic stiffness and tangential stiffness.The nodal flexibility matrix is separated from the overall flexibility matrix.According to the matrix analysis theory,the local coordinate system of the node is established and the flexibility coefficient of each node is obtained.The flexibility of ellipse is used to represent the flexibility of nodes directly,so as to characterize the sensitivity of nodes to external loads.The nodal flexibility of two classical cable domes is compared,and the topological optimum design scheme of the cable dome structure is proposed.It is able to provide a reference for the topological optimization of the dome structure.