Petr Procházka

Design and fabrication of submerged cylindrical laminates—I

Abstract This is the first of a two-part paper concerned with both structural and fabrication process design of a closed-end laminated composite cylinder intended for service in deep sea environment. The cylinder is made of many different orthotropic layers and is loaded by uniform, axisymmetric surface tractions. In addition, piecewise uniform eigenstrains and residual stresses may be caused in the layers during fabrication, by fiber prestress for waviness reduction and by piecewise uniform changes in temperature. The overall goal is to assure efficient use of the composite structure under a prescribed hydrostatic pressure, and to select fiber prestress distribution such that the total stresses in the plies do not exceed certain strength magnitudes. Mechanical and residual stresses in the layers are evaluated with mechanical and transformation influence functions. For the proportional loading applied by a hydrostatic pressure, a procedure is outlined for design of several layups such that the cylinder wall experiences an isotropic in-plane strain and, therefore, all layers support the same compressive normal stresses, regardless of fiber orientation. The results are applied in design and analysis stress fields in a specific structure. Fabrication process design is discussed in the second part of the paper ( Srinivas et al., 1999 , Int. J. Solids Structures, 36, 3945–3976) .

Design and fabrication of submerged cylindrical laminates—II. Effect of fiber pre-stress

Abstract This is the sequel to the first part of this paper ( Dvorak et al., 1999 , Int. J. Solids Structures 36, 3917–3943) , concerned with modeling and analysis of laminated composite cylinder fabrication procedures, such as filament winding or fiber placement, which involve fiber pre-stress for waviness reduction as well as overall or local heating to and cooling from matrix curing temperatures. The fiber pre-stress applied in individual plies is shown to cause a self-stress in the respective plies, and relaxation stresses in the already completed plies and in the supporting mandrel. The final residual stress state is reached after mandrel removal. Influence functions that relate the ply stresses to the applied pre-stress forces are derived. Direct problems are solved for ply stresses caused by prescribed constant or linearly or parabolically changing pre-stress magnitudes in the layers. A superposition of the constant and parabolic distributions is shown to lead to nearly uniform stresses through the cylinder wall. The magnitudes depend on the radial stiffness of the mandrel that supports the structure during fabrication. Inverse problems are formulated as nonlinear optimizations and solved by quadratic programming. The goal is to determine fiber pre-stress distributions through the wall thickness such that the total stresses due to external hydrostatic pressure and fiber pre-stress are as uniform as possible through the wall thickness and confined by the ply strength magnitudes.

Assessment of Laminated Cylindrical Arch Loaded by a Shock Wave

Mutual interaction between a semi-cylindrical arch and the air medium in its neighborhood loaded by a blast or shock wave is the subject of the paper put forward. An impingement of blast wave against structures can cause a reflection of the wave off the surface of the structure followed by a substantial transient aerodynamic load, which can cause a significant deformation of the structure. This deformation can alter the overpressure, which is built behind the reflected shock. In addition, a complex aero-elastic interaction between the blast wave and the structure is developed that can induce a reverberation, which can also cause substantial overpressure through the multiple reflections of the wave. This problem is of particular importance in the new design of future civil, military and underground structures built up from composite materials, as well as of military vehicles.

New Word-Based Adaptive Dense Compressors

In the last two decades the natural language compression made a great progress. The main step in this evolution was the introduction of word-based compression by Moffat. The word-based statistical compression algorithms are able to achieve 35% improvement in the compression ratio in comparison with character-based ones. We present two new word-based statistical compression algorithms based on dense coding idea: Two Byte Dense Code (TBDC) and Self-Tuning Dense Code (SCDC). TBDC uses the codewords with maximal size 2 bytes and must be implemented with some pruning technique. STDC is able to tune its code space during the compression process and so achieve better compression. Our algorithms improve the compression ratio and are considerate to smaller files which are very often omitted. We present also a generalized concept of dense coding called Open Dense Code (ODC) which provides a frame for definition of these two and many other dense code schemas.

Deterministic and stochastic optimization of composite cylindrical laminates

The paper is focused on optimization of prestress and placement of fibers in laminated cylindrical composites. It also involves a stochastic study of prestress deviation in particular layers. Optimization (design) parameters considered in control of internal stresses are the eigenstrains. The behavior of a certain functional serving for optimization of the eigenstrains with stochastically perturbed and correlated values in a laminated cylindrical structure is examined. In the first part, a deterministic optimization of composite laminated cylinders is performed by means of the eigenstrains produced in the layers during the fabrication process. Because fabrication of laminates is sensitive to deviation of eigenstrain magnitudes, as shown from stochastic study, an additional minimization of the eigenstrains is introduced.

A BEM formulation for homogenization of composites with randomly distributed fibers

Abstract In recent papers by the authors, deterministic models of distribution of fibers in composite structures have been studied. For example, problems related to optimization, homogenization, localization, etc., have been solved. The extended Hashin–Shtrikman (H–S) variational principles served as a starting point (eigenparameters were involved in the formulations), and the comparative medium was introduced. The BEM formulations were then admissible and efficient. The formulations of the above-mentioned problems require the restriction of geometry of the fibers to certain ‘locally reasonable’ structures, e.g. to periodic or pseudo-periodic cells. Since the condition of regular distribution of fibers is violated in applications, and a random distribution is more probable, another extension of the H–S principles is needed. In this paper, the problem is extended to the case of statistically distributed fibers. H–S variational principles are formulated in terms of statistical characteristics in the domain and the eigenparameters are also involved, affected by the statistical values. Following the H–S principles, an integral formulation is stated (again, thanks to the use of the comparative medium such a formulation is admissible) in a representative volume, which contains no longer regular geometry of the fibers. The boundary element method has then a special form, which is advantageous particularly for two-phase media. The above-mentioned formulation of H–S variational principles with randomly distributed fields of fibers can be extended to non-linear problems (plasticity, debonding) by introducing transformation fields (eigenstresses or eigenstrains, which are involved in the formulations for completeness). The results form the research presented in this paper basically apply to homogenization of diaphysal implants. But, there is a wide range of applications of the theory introduced in this paper. Due to results from tests on the bearing composite frame of a bicycle, which has a similar structure for certain types of composites of the diaphysal implants, a typical cross-section of the bearing frame of a bicycle is studied as an example. The frame is built of a graphite-epoxy composite.

Homogenization of linear and of debonding composites using the BEM

Abstract A homogenization of microstructure in composites is presented in this paper. Homogenization of composite structures has been solved by many authors, and many numerical methods have been used, particularly when the elastic material behavior of composites was considered. When dealing with linear material properties of such structures, a large background not only in numerical methods but also in mathematical theories are successively developed. A little different situation occurs when in some respect nonlinear material is studied. First, linear problem is solved by the BEM, then we consider possible debond or change of the fiber–matrix interfacial boundary if the debond appears, and both fiber and matrix are elastic. Such a problem is strongly nonlinear. In order to simplify the computations, influence matrices are calculated. Once they are available, Uzawas algorithm can be applied for solving the debonding process.

Shape Optimal Design Using InverseVariational Principles

At present, the optimal shape design of structures is of great importance. Problems of this type mostly lead to very complicated nonlinear systems, and therefore new optimization solutions are being sought. One very efficient tool offers inverse variational principles. It starts with formulation of a variational principle under the assumption that the volume (in the 2D area) of the domain variables is constant. It can easily be shown that then the boundary density of potential energy in the optimal state should be constant too. As the differences of the density of the energy at the boundary nodal points may be very large, the new positions of the boundary nodal points are determined in a special scale. Since inverse variational principles, in connection with the boundary element method, seem to be very prospective for solutions of geometric behavior of homogeneous, and also of partly homogeneous (e.g. phase-wise homogeneous), media, this complex study is presented. To prove the ability of the procedure proposed, two examples are solved at the end of this paper. They are selected in such a way that a comparison with statistically determined and statistically undetermined slender beams, obeying Bernoulli-Euler assumptions, is possible. The examples themselves solve an optimization of stretched plates.

EFFECT OF ELEVATED TEMPERATURE ON CONCRETE STRUCTURES BY BOUNDARY ELEMENTS

Extreme elevation of temperature principally threatens tunnel linings and may cause fatal disaster; the recovery of it may take a long time and significant traffic troubles. System of equations is to be described and solution in terms of boundary element method (BEM) is suggested. Moreover, a technique of time-dependent eigenparameters enables one to apply parallel computations and converts the strongly nonlinear system to pseudo-linear one using the influence and polarization tensors. Consequently, instead of repeated solution of large systems of equations, the multiplication of pre-calculated influence matrices has to be carried out instead. In order to properly create the above-outlined procedure, internal cells are selected in the regions primarily connected by the change of temperature. Some examples follow the theory.

Explosion and Temperature Resistance of Underground Structures by Free Hexagons

It appears that sudden change of loading such as shock wave impinging on underground structures, which is mostly linked up with an extreme increase of temperature, causes immense disasters, which involve loss of human lives, heavy machine damage, long-lasting traffic troubles, decreasing of bearing capacity of the structural system, etc. A combination of shock wave due to both the elevated temperature accompanying explosion leads to cracking of the bearing system of underground openings, for example to cracking of concrete lining, i.e. to reduction of thickness of the bearing structures, etc. It has been previously proved that the free hexagon method serves for identifying the damage in the bearing system of underground structures very well. The dynamical influences have to be also emerged if extreme raise of temperature and explosion are involved in this problem; formulation is briefly mentioned and the results from numerical simulations are presented. It will be shown that the superheated vapor interacting with shock and temperature waves caused by the point charge inside of the underground open space may cause extensive occurrence of fissures on the surface exposed to the external loading envisaged.