THE INCREMENT STIFFNESS MATRIX AND TOTAL QUANTUM STIFFNESS IN NONLINEAR ANALYSES

In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results given in our paper will be of great importance to the analyses of nonlinear numerical and nonlinear stability in finite element methods.

Geometrically Nonlinear Analysis of Structures Using Various Higher Order Solution Methods: A Comparative Analysis for Large Deformation

The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures.The applied methods have a better convergence rate than the quadratic Newton-Raphson method.These six methods do not require higher order derivatives to achieve a higher convergence rate.Six algorithms are developed to use the higher order methods in place of the Newton-Raphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of structures.The higher order methods are applied to both continuum and discrete problems(spherical shell and dome truss).The computational cost and the sensitivity of the higher order solution methods and the Newton-Raphson method with respect to the load increment size are comparatively investigated.The numerical results reveal that the higher order methods require a lower number of iterations that the Newton-Raphson method to converge.It is also shown that these methods are less sensitive to the variation of the load increment size.As it is indicated in numerical results,the average residual reduces in a lower number of iterations by the application of the higher order methods in the nonlinear analysis of structures.

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.