Lars Damkilde

A revised multi-Fickian moisture transport model to describe non-Fickian effects in wood

Abstract This paper presents a study and a refinement of the sorption rate model in a so-called multi-Fickian or multi-phase model. This type of model describes the complex moisture transport system in wood, which consists of separate water vapor and bound-water diffusion interacting through sorption. At high relative humidities, the effect of this complex moisture transport system becomes apparent, and since a single Fickian diffusion equation fails to model the behavior, it has been referred to as non-Fickian or anomalous behavior. At low relative humidities, slow bound-water transport and fast sorption allow a simplification of the system to be modeled by a single Fickian diffusion equation. To determine the response of the system, the sorption rate model is essential. Here the function modeling the moisture-dependent adsorption rate is investigated based on existing experiments on thin wood specimens. In these specimens diffusion is shown to be negligible, allowing a separate study of the adsorption rate. The desorption rate has been observed to be slower at higher relative humidities as well, and an expression analogous to the adsorption rate model is proposed. Furthermore, the boundary conditions for the model are discussed, since discrepancies from corresponding models of moisture transport in paper products have been found.

Lower Bound Limit Analysis Of Slabs With Nonlinear Yield Criteria

A finite element formulation of the limit analysis of perfectly plastic slabs is given. An element with linear moment fields for which equilibrium is satisfied exactly is used in connection with an optimization algorithm taking into account the full nonlinearity of the yield criteria. Both load and material optimization problems are formulated and by means of the duality theory of linear programming the displacements are extracted from the dual variables. Numerical examples demonstrating the capabilities of the method and the effects of using a more refined representation of the yield criteria are given.

Limit state analysis of reinforced concrete plates subjected to in-plane forces

A finite element formulation of rigid-plastic plates subjected to in-plane forces is developed using stress-based elements and linear programming. Three elements are established, namely a triangular plate element, a bar element and a beam element. The problem is formulated as a lower bound solution, and the dual variables are interpreted as displacements. Both load and material optimization are formulated. The method is applied to concrete plate structures modeling both the distributed and the concentrated reinforcement. An efficient computational scheme is used, thereby reducing the size of the problem. Finally, numerical examples are presented to show the capabilities of the method.

Compressive fatigue in wood

Summary An investigation of fatigue failure in wood subjected to load cycles in compression parallel to grain is presented. Small clear specimens of spruce are taken to failure in square wave formed fatigue loading at a stress excitation level corresponding to 80% of the short term strength. Four frequencies ranging from 0.01 Hz to 10 Hz are used. The number of cycles to failure is found to be a poor measure of the fatigue performance of wood. Creep, maximum strain, stiffness and work are monitored throughout the fatigue tests. Accumulated creep is suggested identified with damage and a correlation is observed between stiffness reduction and accumulated creep. A failure model based on the total work during the fatigue life is rejected, and a modified work model based on elastic, viscous and non-recovered viscoelastic work is experimentally supported, and an explanation at a microstructural level is attempted. The outline of a model explaining the interaction of the effect of load duration and the effect of the loading sequences is presented.

A hysteresis model suitable for numerical simulation of moisture content in wood

Abstract The equilibrium moisture content in wood depends not only on the current relative humidity in ambient air, but also on the history of relative humidity variations. This hysteresis dependence of sorption in wood implies that in the worst case the moisture content for a given relative humidity may deviate by 30–35%. While researchers seem to have reached a general agreement on the hypothesis for the sorption hysteresis phenomenon, only a few models describing the phenomenon are available. Current models such as the independent domain model have numerical deficiencies and drawbacks. This paper presents a new hysteresis model, which mathematically resolves in closed-form expressions, with the current relative humidity and moisture content as the only input parameters. Furthermore, the model has the advantage of being applicable to different sorption isotherms, i.e., different species and different temperatures. These features make the model relatively easy to implement into a numerical method such as the finite element method.

LimitS: a system for limit state analysis and optimal material layout

Abstract A system Limits for limit state analysis and material optimization has been developed and implemented in a PC environment. The program is formulated in a general finite element format with stress-based elements. The solution method is based on the lower-bound theorem, where an optimal stress distribution or an optimal material layout is determined. Through linearization of the yield criteria the optimization problem is stated as a linear programming problem. Within the formulation of the discretized model the optimal lower-bound solution is shown to be an upper-bound solution, and thereby both the statics and kinematics of the collapse mode are determined via the dual variables of the LP-problem. In Limits the following element types are implemented: two- and three-dimensional beam elements; truss elements; triangular slab elements; and shear and stringer elements for plates with in-plane loading. Examples of all three problem types are given including both limit state analysis and material optimization.

A flat triangular shell element with Loof nodes

In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiencies are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal configuration of the element is similar to the SemiLoof element, and the formulation is an improvement of a previous formulation. The element is used for both linear statics, linear buckling and geometrical non-linear analysis, and numerical examples are presented to show the robustness, accuracy and quick convergence of the element.

Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method.

method. DTU Orbit (10/08/2019) Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method. Application of the finite element method to Koiters asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical problems and eliminates these problems. The reason for the numerical problems is that the postbuckling stresses are inaccurately determined. By including a local stress contribution, the postbuckling stresses are calculated correctly. The present method gives smooth postbuckling stresses and shows a quick convergence of the postbuckling coefficients

An efficient implementation of limit state calculations based on lower-bound solutions

Abstract Limit state problems are formulated in a general finite element format with stress-based elements. The analysis method is based on the lower-bound theorem which states that stress fields in equilibrium not violating the yield criteria are possible solutions. The solution method is to find the optimal stress distribution which maximizes the load. Linearization of the yield criteria leads to a linear programming problem. In order to have an efficient implementation we have made two improvements compared to previous studies. The first implies that the number of stress parameters are reduced a priori via the equilibrium equations, and the second concerns the linear programming problem, where the traditional non-negative parameter requirement is avoided. The method is described via the plane frame problem but has also been implemented for plates.