Abstract: Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.
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: 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.