Showing papers on "Tangent stiffness matrix published in 2010"

Krylov Subspace Accelerated Newton Algorithm: Application to Dynamic Progressive Collapse Simulation of Frames

Abstract: An accelerated Newton algorithm based on Krylov subspaces is applied to solving nonlinear equations of structural equilib- rium. The algorithm uses a low-rank least-squares analysis to advance the search for equilibrium at the degrees of freedom DOFs where the largest changes in structural state occur; then it corrects for smaller changes at the remaining DOFs using a modified Newton computation. The algorithm is suited to simulating the dynamic progressive collapse analysis of frames where yielding and local collapse mechanisms form at a small number of DOFs while the state of the remaining structural components is relatively linear. In addition, the algorithm is able to resolve erroneous search directions that arise from approximation errors in the tangent stiffness matrix. Numerical examples indicate that the Krylov subspace algorithm has a larger radius of convergence and requires fewer matrix factorizations than Newton-Raphson in the dynamic progressive collapse simulation of reinforced concrete and steel frames. DOI: 10.1061/ASCEST.1943-541X.0000143 CE Database subject headings: Algorithms; Failures; Nonlinear analysis; Progressive collapse; Steel frames. Author keywords: Algorithms; Collapse; Nonlinear analysis; Progressive failure.

Model order reduction for hyperelastic materials

Abstract: In this paper, we develop a novel algorithm for the dimensional reduction of the models of hyperelastic solids undergoing large strains. Unlike standard proper orthogonal decomposition methods, the proposed algorithm minimizes the use of the Newton algorithms in the search of non-linear equilibrium paths of elastic bodies.The proposed technique is based upon two main ingredients. On one side, the use of classic proper orthogonal decomposition techniques, that extract the most valuable information from pre-computed, complete models. This information is used to build global shape functions in a Ritz-like framework.On the other hand, to reduce the use of Newton procedures, an asymptotic expansion is made for some variables of interest. This expansion shows the interesting feature of possessing one unique tangent operator for all the terms of the expansion, thus minimizing the updating of the tangent stiffness matrix of the problem.The paper is completed with some numerical examples in order to show the performance of the technique in the framework of hyperelastic (Kirchhoff-Saint Venant and neo-Hookean) solids.

Mesh Dependence and Nonlocal Regularization of One-Dimensional Strain Softening Plasticity

Abstract: Finite-element analysis of strain localization based on classical theory of continuum mechanics suffers from pathological mesh dependence when strain softening models are used. For quasistatic problems, the mesh dependence is demonstrated through an analysis of the tangent stiffness matrix of a one-dimensional problem. To regularize the mesh dependence, a nonlocal strain softening model is proposed, which is based on the nonlocal plasticity theory and the representative line element. Both analytical and numerical solutions of strain localization with the proposed model are developed and compared with each other. The model is also applied in the numerical simulation of a direct tensile test of a concrete specimen in the existing literature, and reasonable agreement is achieved between numerical solutions and the experimental response.

A mixed co-rotational 3d beam element formulation for arbitrarily large rotations

Abstract: A new 3-node co-rotational element formulation for 3D beam is presented. The present formulation differs from existing co-rotational formulations as follows: 1) vectorial rotational variables are used to replace traditional angular rotational variables, thus all nodal variables are additive in incremental solution procedure; 2) the Hellinger-Reissner functional is introduced to eliminate membrane and shear locking phenomena, with assumed membrane strains and shear strains employed to replace part of conforming strains; 3) all nodal variables are commutative in differentiating Hellinger-Reissner functional with respect to these variables, resulting in a symmetric element tangent stiffness matrix; 4) the total values of nodal variables are used to update the element tangent stiffness matrix, making it advantageous in solving dynamic problems. Several examples of elastic beams with large displacements and large rotations are analysed to verify the computational efficiency and reliability of the present beam element formulation.

A new two-node catenary cable element for the geometrically non-linear analysis of cable-supported structures:

Abstract: This article presents a geometrically non-linear finite-element method for an accurate and efficient analysis of spatial cable structures. A two-node catenary cable element is formulated accurately considering the effect of self-weight of cable element. The tangent stiffness matrix of the cable element is derived as an accurate explicit expression of structural parameters and the nodal forces of the cable element are then also analytically calculated. Pre-stress in the cable element may be considered in the formulation. Three classical numerical examples are first provided to show the accuracy and efficiency of this method and the developed method is then applied to construction stage simulation in order to determine the erection parameters of a suspension bridge through progressive non-linear analysis. The cable element proposed can be conveniently used for the geometric non-linear analysis of flexible structures such as long-span suspension bridges, cable-stayed bridges, and tension structures.

Stiffness modeling for multi-fingered grasping with rolling contacts

Abstract: The stiffness control of an object grasped by a multi-fingered robot hand requires the modeling of the elastic behavior of the object, caused by the stiffness of the fingers. Because of the presence of rolling contacts between the fingers and the object, such a modeling is not a trivial issue, and a very different one from the case of simpler parallel manipulators. We provide here a first expression of the cartesian stiffness matrix produced on the object, as a function of the cartesian stiffness matrices of the fingers, in the case that the contacts are non-sliding point contacts that may freely roll (on the tangent plane) and twist (around the contact normal). We show that this expression of the object-level cartesian stiffness matrix depends also on the contact forces and on the local geometries of the contacting surfaces.

Analysis of masonry structures by funicular networks

Abstract: A numerical approach for the ultimate analysis of large masonry structures composed of multiple linear members is presented. The approach is based on the use of computer-simulated cable nets representing the equilibrium lines (or load paths) that describe the equilibrium condition of structures. Based on this description, limit analysis is applied according to the static approach. Cable net solutions complying with the limit theorems of plasticity – in particular the safe (or lower-bound) and the uniqueness theorems – are generated by means of convenient optimisation techniques. An efficient cable element is adopted with explicit analytical expressions available for the description of the deformed shape in equilibrium and the tangent stiffness matrix. This type of cable element enables the computation of very large cable nets, including a large number of individual cables, with high computational efficiency. The calculation procedure is applied to complex spatial structures and the ability of the techniqu...

Static and free vibration studies on a pulley-belt system with ground stiffness

Abstract: The static and free vibration behavior of a pulley-belt system with ground stiffness is investigated using a nonlinear model based on Hamilton's principle. In the equilibriumanalysis a computational method based on boundary value problem solvers is adapted to obtain the numerical solution, whereas for free vibration analysis spatial discretization is done using the Galerkin's method to evaluate the natural frequencies and vibration modes. The study indicates that there is a considerable decrease in equilibrium deflection due to ground stiffness, especially when it is larger than the belt bending stiffness and this effect is more pronounced for higher values of belt bending stiffness. Equilibrium deflections change reasonably with static span tension variation, but are more sensitive to variations of speed and longitudinal stiffness. The natural frequencies of the pulley-belt system increase with ground stiffness, but this is primarily restricted to the lower modes; higher modes are insensitive to ground stiffness.

Tangent direction controlled subdivision scheme for curve

Abstract: This paper discusses a new non-linear tangent direction controlled subdivision scheme for curve interpolation. Given a sequence of points with their tangent directions, every adjacent pair of points and their tangent directions make a new point and its tangent direction, this operation generates a new sequence of points and their tangent directions, this is one step of subdivision. Repeat this process continuously, this paper proves that the limit of the subdivision operation is a G1 continuous curve, interpolating the given conditions (positions series and their tangent directions). Examples are presented, and some reconstruct circular arcs.

PWL approximation of hyperbolic tangent and the first derivative for VLSI implementation

Abstract: Hyperbolic tangent function is approximated using piecewise linear approximation. This approximation can be used in any embedded hardware architecture where occupied chip space is a challenging factor. The presented recursive algorithm makes a trade-off between circuit delay and accuracy, where low memory consumption is required. In the presented centered linear approximation, hyperbolic tangent and its first derivative is approximated and optimized using maximum error and mean square error of the approximation. Hyperbolic tangent approximation using maximum error shows better results while the first derivative of hyperbolic tangent is better approximated using mean square error. It is demonstrated that a mean square error of 0.02 can be achieved after specific number of iterations in the approximation of hyperbolic tangent.

Direct Stiffness Method

Abstract: High Quality Content by WIKIPEDIA articles! As one of the methods of structural analysis, the direct stiffness method (DSM), also known as the displacement method or matrix stiffness method, is particularly suited for computer-automated analysis of complex structures including the statically indeterminate type. It is a matrix method that makes use of the members' stiffness relations for computing member forces and displacements in structures. The direct stiffness method is the most common implementation of the finite element method (FEM). In applying the method, the system must be modeled as a set of simpler, idealized elements interconnected at the nodes. The material stiffness properties of these elements are then, through matrix mathematics, compiled into a single matrix equation which governs the behaviour of the entire idealized structure. The structure's unknown displacements and forces can then be determined by solving this equation. The direct stiffness method forms the basis for most commercial and free source finite element software. The direct stiffness method originated in the field of aerospace.

Nonlinear analysis of steel tube initial stress effect in stell tube on bearing capacity for CFST arch bridges

Abstract: Based on equilibrium equation of nonlinear problem and nonlinear geometric equation of spatial beam element,explicit formula of tangent stiffness matrix for spatial beam element was deduced,its constitutive relationship includes the initial stress and initial strain.According to structure character of dumbbell section,a combined spatial beam element is presented for computing and storing steel tube initial stress.Method of element division was described about bearing capacity analysis for concrete filled steel tubular(CFST) arch bridge.A special program was developed.The results calculated by program were in accordance with tests.A lot of bearing capacity calculation are performed,with regard to different coefficients of initial stress steel tube,different sectional steel ratios and different spans.Results show that initial stress of steel tube could reduce the capacity of CFST arch bridge,the reduction extent depends on the sectional type of arch rib,and the maximum reduction can exceed 30%.Finally,practical formulas of bearing capacity influence factor are given for the CFST arch bridge with three common sectional types.

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.

Finding the ultimate strength of the titanium alloy spherical pressure shell of a deep-sea submersible using the method of tangent modulus factor

Abstract: A critical step when designing manned deep-sea submersibles is ultimate strength analysis of the pressure shellA method called the tangent modulus factor was appliedIt was derived from the combined theory of strength and stabilityBased on the relationship between stress and strain in a material,the tangent modulus factor curve can be simulated,thus reflecting the structure's balance relationshipThe curve can be expressed also by an analytical function with four parametersThe function was used to calculate the ultimate strength of a titanium alloy spherical pressure shell for a deep-sea submersibleThese results were compared with those from the Taylor Basin formula and the finite element methodThe method proposed in this paper is simpler and the results showed that it produces figures acceptable for engineering practiceThis showed that the tangent modulus factor method is valid for preliminary design and analysis of proposed spherical shell pressure hulls

Nonlinear stability bearing capacity analysis for a suspended dome based on the initial curvature elements

Abstract: In the element follow-up coordinate system,the computation formulation considering the influence of initial curvature on the link element is established,and the element stiffness matrix including the effect of initial curvature is derived.Then the tangent stiffness matrix of initial curvature beam element is deduced base on classical beam-column theory.Finally,the nonlinear stability bearing capacity analysis is carried out for the suspended dome structure by using the initial curvature link and beam element,and the influence of the member initial curvature on the structural nonlinear stability performance is investigated.The results show that the structural stiffness and limited bearing capacity are reduced since the member initial curvature exists.In different initial prestressing states,the limit load is linearly reduced with the increase of initial curvature and the relation curves between them are parallel.The proposed initial curvature element in this paper can be generally applied into the nonlinear analysis of various kinds of space grid structures,which provides more scientific accordance for the structural design.

Advanced analysis of plane steel frame having imperfect elements

Abstract: Imperfect elements having initial curvature are usually used in construction and erection of the structures. In this paper, the explicit stiffness matrix for imperfect element is derived. The nonlinear tangent stiffness matrix of the beam-column subjected to the axial force, nodal moments and the lateral uniformly distributed load is calculated. Based on this matrix, advanced analysis of the plane steel frame is performed. Both tensile and compressive axial loads are also taken into account by one formula. By using the proposed stiffness matrix, the load-displacement curve is compared with the accurate plastic region methods, and in the most cases, good agreement is found. Comparing the obtained results with other references shows the accuracy and capabilities of the new formulation in evaluation of the steel frame load capacity having inelastic second-order behavior.

Development of corotational formulated FEM for application to 30m class large deployable reflector

Abstract: JAXA, Japan Aerospace Exploration Agency, is now developing a corotational formulated finite element analysis method and its software Origami/ETS for the development of 30m class large deployable reflectors. For the reason that the deployable reflector is composed of beams, cables and mesh, this analysis method is generalized for finite elements with multiple nodes, which are commonly used in linear finite element analyses. The large displacement and rotation are taken into account by the corotational formulation. The tangent stiffness matrix for finite elements with multiple nodes is obtained as follows; the geometric stiffness matrix of two node elements is derived by taking variation of the element's corotational matrix from the virtual work of finite elements with large displacement; similarly the geometric stiffness matrix for three node elements is derived; as the extension of two and three node element theories, the geometric stiffness matrix for multiple node elements is derived; with the geometric stiffness matrix for multiple node elements, the tangent stiffness matrix is obtained. The analysis method is applied for the deployment analysis and static structural analysis of the 30m class large deployable reflector. In the deployment analysis, it is confirmed that this method stably analyzes the deployment motion from the deployment configuration to the stowed configuration of the reflector. In the static analysis, it is confirmed that the mesh structure is analyzed successfully. The 30m class large deployable reflector is now still being developed and is about to undergo several tests with its prototypes. This analysis method will be used in the tests and verifications of the reflector.

Notice of Retraction An improved predictor-corrector procedure for the dynamics of geometrically nonlinear shell structure

Abstract: For geometrically nonlinear structure, the expressions of tangent stiffness matrix and internal forces of shell element are derived by CR (Co-rotational) theory, and the simplified formulation is performed on static analysis of a hinged cylindrical segment and validated by the results of experiment and references. Then, a predictor-corrector procedure with an approximately energy conservation is developed. With the application on nonlinear symmetric motion of a cylinder under two pinching forces, the improved procedure presents a better stability and accuracy than nonlinear Newmark algorithm.

A new nonlinear soil constitutive model based on hyperbolic tangent function

Abstract: A new nonlinear soil constitutive model based on hyperbolic tangent function is presented,in which the shape of proposed backbone curve is the same as that of the hyperbolic tangent function curve shifted and enlarged by two factors.Such new model is expressed in a simple form and has a straightforward physical meaning.It can be executed by the computer without large computer memory.The only thing needs to be done for obtaining hysteresis loop is the determination of original shear strain and shear stress values at the beginning of unloading and reloading.Efforts have also been made in the seismic ground response analysis with a program developed based on this new stress-strain model.Results comparison with that carried out by the equivalent linear method shows that it is feasible to use this new constitutive model in seismic ground response analysis.Practical significance is of interest to develop such nonlinear soil constitutive model.

Stability analysis for 3D frames using mixed corotational formulation

Abstract: The corotational technique is adopted for the analysis of 3D beams The technique applies to a two-noded element a coordinate system which continuously translates and rotates with the element In this way, the rigid body motion is separated out from the deformational motion Then, a mixed formulation is adopted for the derivation of the local element tangent stiffness matrix and nodal forces The mixed finite element formulation is based on an incremental form of the two-field Hellinger-Reissner variational principle to permit elasto-plastic material behavior The proposed element can be used to analyze the nonlinear buckling and postbuckling of 3D beams The mixed formulation solution is compared against the results obtained from a corotational displacement-based formulation having the same beam kinematics The superiority of the mixed formulation is clearly demonstrated

Application Analysis of an Improved N-R Iterative Method about Finite Element Numerical Calculation

Abstract: During the numerical calculation by FE (Finite Element) method, N-R (Newton-Raphson) iterative method will be used to solve the problem such that material performing with elasto-plastic character and geometric non-linearity. However, if the problem has macro scale DOFs (degree of freedom), the classical N-R method is shown to make a low efficiency on the whole process. For this reason, in this paper, an improved N-R iterative method is proposed by creating proper mandatory limiters to change the step size of displacement field increment. In this way, the size of single iterative step is enlarged in the new method with tangent stiffness matrix used as classical N-R iterative theory as well. Furthermore, to test stability of the new method, two models of structure are chosen to be calculated with this method. In the conclusion, the improved N-R iterative method is indicated to be an efficient and stable numerical method which could solve nonlinear problems, especially with macro scale DOFs.

Closed-loop stiffness modeling and stiffness performance analysis for multi-axis process system

Abstract: General stiffness performance of manufacturing process system directly affects machining accuracy and stability. When machining complex surface, general stiffness performance changes with tool posture that is determined by machining position and feed direction. In order to analyze general stiffness performance including machine tool, cutter and workpiece, a closed loop stiffness model is established by Jacobi matrix and finite element method. It is a general stiffness model for multi-axis process system, which can be used to evaluate general stiffness performance in workspace. The distribution law of stiffness performance can be evaluated by isoclines map of stiffness index plotted in workpiece coordinate system. The result helps engineers plan tool path based on both geometric and physics constrains.

The role of the tangent bundle for symmetry operations and modulated structures.

Abstract: An equivalence relation on the tangent bundle of a manifold is defined in order to extend a structure (modulated or not) onto it. This extension affords a representation of a structure in any tangent space and that in another tangent space can easily be derived. Euclidean symmetry operations associated with the tangent bundle are generalized and their usefulness for the determination of the intrinsic translation part in helicoidal axes and glide planes is illustrated. Finally, a novel representation of space groups is shown to be independent of any origin point.