Uniform Strain Energy Density Research Articles

Topology and fibre orientation simultaneous optimisation: A design methodology for fibre-reinforced composite components

Additive manufacturing for fibre-reinforced composite structures is rapidly diffusing, since it enables the production of lightweight structural parts characterized by complex geometries and tailored fibre orientations. Therefore, the development of design methodologies capable to simultaneously optimize the shape of the fibre-reinforced composite part and the fibre orientation in the additive manufacturing process is, at present, of utmost interest among industries and research centres. In this paper, a novel simultaneous optimisation method capable to optimise the topology and the local fibre orientation is proposed. The method is computationally cheap, fast convergent and permits to avoid stress peaks, working efficiently on 2D and on 3D models. The analytical formulation of the problem and the optimisation algorithm are at first described. The optimisation criteria are based on the uniform strain energy density distribution and the fibre alignement along the principal stress direction. The proposed method is then verified with several benchmarks from the literature and with a 3D illustrative example, confirming that it can be effectively and efficiently employed for the optimisation of composite components to be produced through additive manufacturing.

Soundness Discrimination in Ferrite Ductile Irons Through Tensile Data Analysis

Ferritic ductile iron (DI) GJS 400 and high-silicon strengthened ductile irons (HSSDIs) with 3.5 and 4.5 wt% of silicon contents were produced with different cooling rates, and the microstructures were analyzed to find the main microstructure parameters. The Y-blocks GJS 400 presented good nodularity, while the heavy section GJS 400 presented some graphite degeneracy with a lower nodularity. The 3.5 wt% HSSDI shown a good nodularity, while with increasing silicon content to 4.5 wt%, significant graphite degeneracy occurred with the appearance of chunky graphite. Samples were tensile tested and the tensile data were analyzed through the physical-based constitutive Voce equation, and the Voce parameters were plotted to produce a matrix assessment diagram (MAD). Y-blocks and heavy section GJS 400 data lied on two distinct lines in MAD, and they had, however, positive and negative intercepts which meant indeed two contradictory plastic behaviors. The intercept of the best fitting line of the GJS 400 Y-blocks data was positive and so consistent with the physical meaning of Voce equation, while the intercept of the best fitting line of the GJS 400 heavy section data was negative, which meant an unexpected opposite plastic behavior. Same behavior was reported for the investigated HSSDIs, resulting in positive intercept of the best fitting line in MAD for the 3.5 wt% HSSDI data and negative intercept for the 4.5 wt% HSSDI data. The uniform strain energy density (SEDU) that is the area below the tensile flow curve up to the uniform strain, i.e., the strain where necking begins, was also investigated. SEDU resulted to be almost constant for all the GJS 400 Y-blocks tensile flow curves and 3.5 wt% HSSDI, which was typical of a sound material, while in GJS 400 heavy section and 4.5 wt% HSSDI, SEDU changed significantly in a systematic way, indicating that metallurgical defects had affected the plastic behavior. So it was concluded that in the MAD the best fitting line of the tensile data with positive intercept was a possible indication of the material soundness, while the negative intercept was indication of defected material. The results suggested that the MAD analysis produced from tensile Voce parameters can be a useful and easy tool for industry not only to classify the production routes of DIs (Si content mainly and heat treatments), but also to identify possible microstructure poorness within a single DI grade.

Composite Structure Design of O-Rings Using Material Behavior to Decrease Strain Energy and Permanent Deformation

The performance of elastomeric seals degrades over time in use due to the development of permanent material deformation. The existence of localized high stress regions below seal-housing contact areas led to consideration of improving O-ring design by modifying material behavior to decrease strain energy, and so permanent deformation, in these regions. Photoelastic stress analysis was used to experimentally characterize the stress and strain fields in O-ring sections and to validate finite element models used in design studies. O-ring section designs that included small inset regions of different material behavior than the larger surrounding section were investigated with the intent of manipulating and reducing the strain energy content. Finite element models of O-rings were used to characterize the strain energy content and distribution for inset materials with various stress-strain behaviors. Measurements of permanent deformation and load-deflection behavior of specimens held under applied compression over time showed dependence of the amount of permanent deformation on strain energy. Design rules were extracted from results of studies in which inset region material stiffness, stress-strain behavior, size, and location in the larger section were varied. O-ring sections with regions of less stiff material result in lower strain energy and more uniform strain energy density distribution than the typical one-material seal. Inclusion of less stiff softening stress-strain behavior material insets in the larger O-ring section produced reduction in strain energy level and favorable redistribution of the high strain energy density regions compared with the conventional one-material one-material-behavior design. Similar concepts will apply to the design of other elastomeric structures in which permanent material deformation affects structure performance.

Optimality Conditions of the Hybrid Cellular Automata for Structural Optimization

The hybrid cellular automaton method has been successfully applied to topology optimization using a uniform strain energy density distribution approach. In this work, a new set of design rules is derived from the first-order optimality conditions of a multi-objective problem. In this new formulation, the final topology is derived to minimize both mass and strain energy. In the hybrid cellular automaton algorithm, local design rules based on the cellular automaton paradigm are used to efficiently drive the design to optimality. In addition to the control-based techniques previously introduced, a new ratio technique is derived in this investigation. This work also compares the performance of the control strategies and the ratio technique.

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.

Experimental determination of J on rubbery materials: Influence of finite dimensions

Expression of the energetic parameter J proposed by Andrews is re-examined and the influence of specimen dimensions is introduced, leading to a general expression of the form J = H( W 0) · G( a/ w), where W 0 is uniform strain energy density and a and w are, respectively, crack length and width of the specimen. This relation gives an overview of the respective influences of material behaviour and finite dimensions. Using three kinds of specimen geometry, results obtained from fracture tests on an EPDM-based polymer indicate clearly that the calibration factor derived from G( a/ w) (depending on the geometry) is significantly affected by non-linearity since it was found to be really different from the linear equivalent one. Furthermore, the single edge notch tension (SENT) and central cracked (CC) specimens lead to a similar distribution function k( W 0) = H( W 0)/ w 0, while the result for a pure shear specimen is different. This is mainly a consequence of the uniform strain energy density distribution which is, respectively, force or displacement controlled.

Comparison of Two Types of Structural Optimization Procedures for Flutter Requirements

A comparison is made of results obtained from mathematical programing and optimality criteria procedures for the minimum-mass design of typical aircraft wing structures to satisfy prescribed flutter requirements. The mathematical programing method is based on an interior penalty function approach. A Langrangian optimality criterion and an intuitive optimality criterion based on uniform strain energy density are considered. An intuitive resizing procedure is used for both optimality criterion solutions. All results are calculated using the same computer program, changing only the optimization procedure. Both high- and low-aspect-ratio wings are examined. Finite elements are used for structural modeling, and the generalized coordinates for the flutter solution are based on the natural vibration modes of the structure. Second-order piston theory aerodynamics is used for supersonic conditions and kernel function aerodynamics for subsonic conditions. Convergence of the optimality criteria procedures with respect to the number of natural modes is considered. [A ] [B] [Bti] Nomenclature