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The propagation of elastic plane waves in orthotropic incompressible materials is examined under plane strain conditions in a plane of symmetry. The slowness surface is obtained by aligning a material axis of symmetry with the direction of minimum phase speed. The existence of incident homogeneous waves and reflected homogeneous and nonhomogeneous waves in the presence of a planar interface separating two half-spaces is subsequently examined. A surface which separates the range of existence of two homogeneous reflected waves from that of one homogeneous and one nonhomogeneous is obtained in terms of the angle of incidence, the orientation of the interface with respect to the material axis of symmetry, and one elastic parameter. The critical orientation beyond which there exist two homogeneous reflected waves is derived in explicit form in terms of the elastic parameter. Reflection coefficients are obtained and discussed when the interface is a free surface. Exclusion points are defined in the range of existence of the reflected waves as points for which only one reflected (homogeneous) wave exists. The analysis is complemented with numerical examples.

We analyze the effect of anisotropy on beam flexibility by the derivation of upper and lower bounds, through use of the principles of minimum potential and complementary energy, for the load-deflection ratios of narrow rectangular cross-section cantilever beams. The basic assumption is a class of stress-strain relations of such nature that normal strains are caused not only by normal stresses but also by shearing stresses, and shearing strains are caused not only by shearing stresses but also by normal stresses.

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The performance of wind turbine blades can be affected by conditions such as sand concentration in dry dusty environments. The mathematical formulations for continuum phase (air) and discrete phase (sand particles) along with the imposed assumptions and applied boundary conditions are presented in this paper. The numerical simulation conducted in this paper studied the effect of sand particles on flow structure and essential dimensionless numbers for flow over the primary airfoil of the wind turbine. The effects of controlling parameters such as sand dimensions, sand/air drift velocity and sand/air mass flow rate ratio are studied and the results are compared against the conditions of uniform, far-field air flow. The results are presented in terms of pressure distribution over the airfoil surface, drag and lift coefficients along with variation of erosion and accretion due to the collision of sand particles over the airfoil surface for various attack angles.

The heat conduction and the moving solid-liquid interface in a finite region is studied numerically. A Fourier series expansion is used in both phases for spatial temperature distribution, and the differential equations are converted to an infinite number of ordinary differential equations in time. These equations are solved iteratively for the interface location as well as for the temperature distribution. The results are compared with existing solutions for low Stefan numbers. New results are presented for higher Stefan numbers for which solutions are unavailable.

This textbook treats solids and fluids in a balanced manner, using thermodynamic restrictions on the relation between applied forces and material responses. This unified approach can be appreciated by engineers, physicists, and applied mathematicians with some background in engineering mechanics. It has many examples and about 150 exercises for students to practise. The higher mathematics needed for a complete understanding is provided in the early chapters. This subject is essential for engineers involved in experimental or numerical modelling of material behaviour.