Tangent stiffness matrix

About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.

Analysis of large deflection of nanobeams based on the modified couple stress theory by using finite element method

Abstract: A total Lagrangian finite element formulation was developed for investigating large deflection bending of nanobeams based on the modified couple stress theory. Timoshenko beam theory accompanied by the axial displacement with least kinematic assumptions has been used to model nanobeams. For the first time, the tangent stiffness matrix for nanobeams is extracted based on the modified couple stress theory. The present finite element formulation provides the possibility of solving the problems of nanobeams with arbitrary loading, boundary conditions and cross-sectional variation. The obtained results have been validated with the results reported in the other works. The influence of material length scale parameter on the maximum amount of displacement and rotation of nanobeams is discussed for different ratios of the nanobeam length to the thickness. Besides, for the illustration of abilities of the present formulation, large deflection of a tapered nanobeam under the sinusoidal distributed load for two types of boundary conditions (clamped and simply supported) has been presented.

Beam element for large displacement analysis of elasto-plastic frames

Abstract: ABSTRA CT. The present paper develops a non-linear beam element for analysis of elastoplastic frames under large displacements. The finite element formulations are derived by using the co-rotational approach and expression of the virtual work. The Gauss quadrature is employed for numerically computing the element tangent stiffness matrix and internal force vector. A bilinear stress-strain relationship with isotropic hardening is adopted to update the stress. The arc-length technique based on the Newton-Raphson iterative method is employed to compute the equilibrium paths. A number of numerical examples is employed to assess the performance of the developed element. The effects of plastic action on the large displacement behavior of the structures as well as the expansion of plastic zones in the loading process are discussed.

A Method of Stiffness Analysis of Parallel Mechanisms

Abstract: This paper presents a method, called Parameter-Separation Method, for stiffness analysis of parallel mechanisms. By treating the effect of different parameters (i.e. external force and torque, translational and rotational displacement) separately, the method produces 4 criteria of stiffness analysis. A further method based on the first method is proposed when we conduct stiffness analysis on some parallel mechanisms whose inputs are of the same unit. It applies a special way to formulate dimensionally homogeneous Jacobian matrix with consideration of the input need, and comes up with 2 criteria to judge the stiffness of parallel mechanisms. These two methods are explained in detail, and their effects and relationship are demonstrated by stiffness analysis of a 4RRR redundantly actuated parallel mechanism.

Influence of Excitation Amplitude and Load on the Characteristics of Quasi-zero Stiffness Isolator

Abstract: An Euler buckled beam formed negative stiffness mechanism is proposed and the static characteristic of which is analyzed.A quasi-zero stiffness isolator is designed by parallel connecting the negative stiffness mechanism and a linear isolator.The Euler buckled beam structure functions as a stiffness corrector to lower the stiffness of the linear isolator.If the load is chosen properly,the equilibrium point will be set at the zero stiffness point,any changes of the load will lead the equilibrium point deviating from the zero stiffness point.The dynamic model is built considering the load effect and the harmonic balance method is employed to solve for the dynamic response of the system.Force transmissibility of the zero guasi-stiffness isolator is defined and compared with that of an equivalent linear one.The effect of excitation amplitude and load on the performance is analyzed.The results show that the force excitation amplitude and load can change the characteristic of the nonlinear isolator from a hardening stiffness system to a softening stiffness system and even a mixed softening-hardening stiffness system.The excitation amplitude and load also have great affection on the transmissibility performance.

Resistance of the pavement to water and frost in the cold recycling technology

Abstract: The road pavement structure (apart from having the required load capacity) should be water and frost resistant. This is important for pavements produced with the cold recycling technology. Foamed bitumen and, alternatively, bitumen emulsion were used for the resistance tests of the pavements. The bitumen binder content in the recycled material was 2.0%, 2.5% and 3.0%. The tests (stability against deformation, Marshall stiffness and indirect tensile strength (ITS)) showed that use of foamed bitumen is more advantageous than bitumen emulsion. That is in terms of mechanical properties of pavement. The measurements of resistance due to water and frost (according to AASHTO T283 method) and resistance to low temperature cracking (according to the PANK 4302 method) confirmed that pavement produced with the cold recycling technology is resistant to these climatic factors. The tests also showed that pavement produced with foamed bitumen is more resistant than pavement with bitumen emulsion. It is suggested, that general water resistance criterion (tensile strength retained (TRS)) of such pavement should be broadened to include e.g. the AASHTO T283 method.