Abstract: Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.
Abstract: This paper develops a method for considering the critical fatigue stress as a constraint in the Bi-directional Evolutionary Structural Optimization (BESO) method. Our aim is to reach an optimal design in which high cycle fatigue failure does not occur for a specific life time. The critical fatigue stress is calculated based on modified Goodman criteria and used as a stress constraint in our topology optimization problem. Since fatigue generally does not occur for compressive stresses, we use the p-norm approach of the stress measurement that considers the highest tensile principal stress in each point as stress measure to calculate the sensitivity numbers. The BESO method has been extended to minimize volume an object subjected to the critical fatigue stress constraint. The optimization results are compared with the results from the compliance minimization problem which shows clearly the merits of our newly developed approach.
Abstract: Strength and deformability characteristics of a liquefiable sand deposit including the development of earthquake-induced shear stress and shear strain as well as soil softening via the progressive degradation of shear modulus were studied via shaking table experiments. To do so, a model of a liquefiable sand deposit was constructed and densely instrumented where accelerations, pressures, and displacements at different locations were continuously monitored. Furthermore, the confinement effects on the strength and deformation characteristics of the liquefiable sand deposit due to an external surcharge by placing a heavy concrete slab (i.e. the model of an actual structural rigid pavement) on the ground surface were examined. The results indicate that as the number of seismic-loading cycles increases, the sand deposit softens progressively as large shear strains take place in different sand elements. Liquefaction state is reached after the combined effects of the progressive degradation of the initial shear modulus associated with the continuous decrease in the mean principal stress, and the buildup of the excess of pore pressure takes place in the sand deposit. Finally, the confinement effects given by a concrete slab placed on the surface of the sand deposit resulted in a favorable increasing in the initial shear modulus, an increase in the mean principal stress and a decrease in the softening rate (i.e. the decreasing rate in shear modulus) of the sand, thus making the onset of liquefaction to take place at a later stage. This is, only after the sand deposit having a concrete slab experienced a higher number of seismic loading cycles liquefaction took place, in contrast to an ordinary sand deposit having no concrete slab.
Abstract: In order to achieve the layout and size optimization of the web members of tower crane boom, a truss topology and cross section size optimization method based on continuum is proposed considering three typical working conditions. Firstly, the optimization model is established by replacing web members with web plates. And the web plates are divided into several sub-domains so that periodic soft kill option (SKO) method can be carried out for topology optimization of the slender boom. After getting the optimized topology of web plates, the optimized layout of web members is formed through extracting the principal stress distribution. Finally, using the web member radius as design variable, the boom compliance as objective and the material volume of the boom as constraint, the cross section size optimization mathematical model is established. The size optimization criterion is deduced from the mathematical model by Lagrange multiplier method and Kuhn-Tucker condition. By comparing the original boom with the optimal boom, it is identified that this optimization method can effectively lighten the boom and improve its performance.
Abstract: Anisotropy is one of the major aspects that affect soil behavior, and extensive efforts have investigated its effect on the mechanical properties of soil. However, very little attention has been given to the combined effect of anisotropy and fine contents. Therefore, in this paper, the anisotropic strength of sand containing different fine content (F) of 5%, 10%, 15%, and 20%, was investigated using hollow cylinder tests under different principal stress directions of α = 0° and α = 90°. For a given principal stress direction (α), it was found that increasing fine content resulted in decreasing deviator stress (q). Moreover, results revealed that all fine contents showed anisotropic strength where there is a clear difference between the strength under 0° and the strength under 90°. This anisotropy was greatest under F = 5% while it decreased with increasing fine contents, particularly at F = 10%. Mixtures with low fine content show low contractive behavior and tended to show more dilation. Moreover, all sand-clay mixtures exhibited less dilation and more compression at α = 90° compared with that at α = 0°.
Abstract: Ball joints support and guide certain automotive parts that move relative to the frame of the vehicle. Such ball joints are covered and protected from dust, mud, and other interfering materials by ball-joint boots made of rubber—a flexible and near-incompressible material. The boots may experience twisting and bending deformations because of the motion of the joint arm. Thus, environmental and endurance tests of ball-joint boots apply both bending and twisting deformations. In this study, environmental and endurance testing was simulated via the finite element method performed by using a commercial software package. The ranges of principal stress and principal strain values that are known to directly affect the fatigue lives of the parts were sought. By defining these ranges, the number of iterative tests and modifications of the materials and dimensions of the boot can be decreased. Therefore, instead of performing actual part tests, manufacturers can perform standard fatigue tests in trials of different materials by applying only the defined range of stress or strain values.
Abstract: In this paper, von Mises and Drucker-Prager yield criteria, as typical ones that consider the effect of intermediate principal stress σ2, have been selected and employed for investigating the influence of σ2 on the solution of a typical stability problem. The bearing capacity factors have been calculated under plane strain condition (strip footing) and axisymmetric condition (circular footing) using the method of stress characteristics together with the criteria mentioned. Different levels of σ2 relative to the other two principal stresses have been considered. While a higher σ2 entry in yield criterion gives a higher bearing capacity; its entry in equilibrium equations (axisymmetric) causes substantial reduction.
Abstract: The global solved problem is the calculation of the
parameters of ceramic material from a set of destruction tests of
ceramic heads of total hip joint endoprosthesis. The standard way of
calculation of the material parameters consists in carrying out a set of
3 or 4 point bending tests of specimens cut out from parts of the
ceramic material to be analysed. In case of ceramic heads, it is not
possible to cut out specimens of required dimensions because the
heads are too small (if the cut out specimens were smaller than the
normalised ones, the material parameters derived from them would
exhibit higher strength values than those which the given ceramic
material really has). A special destruction device for heads
destruction was designed and the solved local problem is the
modification of this destructive device based on the analysis of
tensile stress in the head for two different values of the depth of the
conical hole in the head. The goal of device modification is a shift of
the location with extreme value of σ1max from the region of head’s
hole bottom to its opening. This modification will increase the
credibility of the obtained material properties of bioceramics, which
will be determined from a set of head destructions using the Weibull
weakest link theory.
Abstract: This article aims to study the effect of pressure on rocket motor case by Finite Element Method simulation to select optimal material in rocket motor manufacturing process. In this study, cylindrical tubes with outside diameter of 122 mm and thickness of 3 mm are used for simulation. Defined rocket motor case materials are AISI4130, AISI1026, AISI1045, AL2024 and AL7075. Internal pressure used for the simulation is 22 MPa.
The result from Finite Element Method shows that at a pressure of 22 MPa rocket motor case produced by AISI4130, AISI1045 and AL7075 can be used. A comparison of the result between AISI4130, AISI1045 and AL7075 shows that AISI4130 has minimum principal stress and confirm the results of Finite Element Method by the used of calculation method found that, the results from Finite Element Method has good reliability.
Abstract: Complex sensitivity analysis of stresses in a concrete slab of the real type of rigid pavement made from recycled materials is performed. The computational model of the pavement is designed as a spatial (3D) model, is based on a nonlinear variant of the finite element method that respects the structural nonlinearity, enables to model different arrangements of joints, and the entire model can be loaded by the thermal load. Interaction of adjacent slabs in joints and contact of the slab and the subsequent layer are modeled with the help of special contact elements. Four concrete slabs separated by transverse and longitudinal joints and the additional structural layers and soil to the depth of about 3m are modeled. The thickness of individual layers, physical and mechanical properties of materials, characteristics of joints, and the temperature of the upper and lower surface of slabs are supposed to be random variables. The modern simulation technique Updated Latin Hypercube Sampling with 20 simulations is used. For sensitivity analysis the sensitivity coefficient based on the Spearman rank correlation coefficient is utilized. As a result, the estimates of influence of random variability of individual input variables on the random variability of principal stresses s1 and s3 in 53 points on the upper and lower surface of the concrete slabs are obtained.
Abstract: In this study rack systems that are structural storage
units of warehouses have been analyzed as structural with Finite
Element Method (FEA). Each cell of discussed rack system storages
pallets which have from 800 kg to 1000 kg weights and
0.80x1.15x1.50 m dimensions. Under this load, total deformations
and equivalent stresses of structural elements and principal stresses,
tensile stresses and shear stresses of connection elements have been
analyzed. The results of analyses have been evaluated according to
resistance limits of structural and connection elements. Obtained
results have been presented as visual and magnitude.
Abstract: In the paper the results of calculations of the dynamic
response of a multi-storey reinforced concrete building to a strong
mining shock originated from the main region of mining activity in
Poland (i.e. the Legnica-Glogow Copper District) are presented. The
representative time histories of accelerations registered in three
directions were used as ground motion data in calculations of the
dynamic response of the structure. Two variants of a numerical model
were applied: the model including only structural elements of the
building and the model including both structural and non-structural
elements (i.e. partition walls and ventilation ducts made of brick). It
turned out that non-structural elements of multi-storey RC buildings
have a small impact of about 10 % on natural frequencies of these
structures. It was also proved that the dynamic response of building
to mining shock obtained in case of inclusion of all non-structural
elements in the numerical model is about 20 % smaller than in case
of consideration of structural elements only. The principal stresses
obtained in calculations of dynamic response of multi-storey building
to strong mining shock are situated on the level of about 30% of
values obtained from static analysis (dead load).
Abstract: In this survey the process of crack propagation at the
toe of concrete gravity dam is investigated by applying principals
and criteria of linear elastic fracture mechanic. Simulating process of
earthquake conditions for three models of dam with different
geometrical condition, in empty reservoir under plain stress is
calculated through special fracture mechanic software FRANNC2D
[1] for determining fracture mechanic criteria. The outcomes showed
that in spite of the primary expectations, the simultaneous existence
of fillet in both toe and heel area (model 3), the rate of maximum
principal stress has not been decreased; however, even the maximum
principal stress has increased, so it caused stress intensity factors
increase which is undesirable. On the other hand, the dam with heel
fillet has shown the best attitude and it is because of items like
decreasing the rates of maximum and minimum principal stresses and
also is related to decreasing the rates of stress intensity factors for 1st
& 2nd modes of the model.
Abstract: Complex statistical analysis of stresses in concrete
slab of the real type of rigid pavement is performed. The
computational model of the pavement is designed as a spatial (3D) model, is based on a nonlinear variant of the finite element method
that respects the structural nonlinearity, enables to model different arrangement of joints, and the entire model can be loaded by the
thermal load. Interaction of adjacent slabs in joints and contact of the slab and the subsequent layer are modeled with help of special
contact elements. Four concrete slabs separated by transverse and
longitudinal joints and the additional subgrade layers and soil to the depth of about 3m are modeled. The thickness of individual layers,
physical and mechanical properties of materials, characteristics of
joints, and the temperature of the upper and lower surface of slabs are supposed to be random variables. The modern simulation technique
Updated Latin Hypercube Sampling with 20 simulations is used for statistical analysis. As results, the estimates of basic statistics of the
principal stresses s1 and s3 in 53 points on the upper and lower surface of the slabs are obtained.