An optimization framework is developed to minimize structural weight of the front-frame of heavy-duty trucks while satisfying stress constraint. The shape of the frame is defined by a number of design parameters (which define the shape of the side-rail, position and width of the internal brackets, and width of the flanges). In addition, the thickness of the engine-mount, the side-rails, inner-brackets, radiator mount, shock absorber and cab-mount connector are also considered as design variables. Aluminum Alloy, 6013-T6 is chosen as the material and the maximum allowable stress is the yield stress (320 MPa). A quantity known as ‘Violation’ is defined as the ratio of area in the front-end module where stress constraint is violated to the total area of the frame is introduced to implement stress constraints. For optimization, the penalty method is used where the objective is to minimize the total weight while keeping the value of the ‘Violation’ parameter less than 0.1 %. The Particle Swarm Optimization Algorithm is implemented using parallel computation for optimizing the structure. Commercial FEA software MSC.PATRAN is used for creating the geometry and the mesh whereas MSC.NASTRAN is used to perform static analysis. Six design load conditions, each corresponding to a road condition are used for the problem.

No abstract

This paper presents a general approach for the free vibration analysis of curvilinearly stiffened rectangular and quadrilateral plates using the Ritz method by employing classical orthogonal Jacobi polynomials. Both the plate and stiffeners are modeled using first-order shear deformation theory (FSDT). The displacement and rotations of the plate and stiffeners are approximated by separate sets of Jacobi polynomials. The ease of modification of the Jacobi polynomials enables the Jacobi weight function to satisfy geometric boundary conditions without loss of orthogonality. The distinctive advantage of Jacobi polynomials, over other polynomial-based trial functions, lies in that their use eliminates the well-known ill-conditioning issues when a high number of terms are used in the Ritz method, e.g., to obtain higher modes required for vibro-acoustic analysis. In this paper, numerous case studies are undertaken by considering various sets of boundary conditions. The results are verified both with the detailed finite element analysis (FEA) using commercial software msc.nastran and with those available in the open literature. New formulation and results include: (i) exact boundary condition enforcement through Jacobi weight function for FSDT, (ii) formulation of quadrilateral plates with curvilinear stiffeners, and (iii) use of higher order Gauss quadrature scheme for required integral evaluations to obtain higher modes. It is demonstrated that the presented method provides good numerical stability and highly accurate results. The given new numerical results and convergence studies may serve as benchmark solutions for validating the new computational techniques.

No abstract

This paper presents a general approach for the free vibration analysis of curvilinearly stiffened rectangular and quadrilateral plates using Ritz method employing classical orthogonal Jacobi polynomials. Both the plate and stiffeners are modeled using first-order shear deformation theory (FSDT). The displacement and rotations of the plate and a stiffener are approximated by separate sets of Jacobi polynomials. The ease of modification of the Jacobi polynomials enables the Jacobi weight function to satisfy geometric boundary conditions without loss of orthogonality. The distinctive advantage of Jacobi polynomials, over other polynomial-based trial functions, lies in that their use eliminates the well-known ill-conditioning issues when a high number of terms are used in the Ritz method; e.g., to obtain higher modes required for vibro-acoustic analysis. In this paper, numerous case studies are undertaken by considering various sets of boundary conditions. The results are verified both with the detailed Finite Element Analysis (FEA) using commercial software MSC.NASTRAN and for some cases, and with those available in the open literature for others. Convergence studies are presented for studying the effect of the number of terms used on the accuracy of the solution. The paper also discusses the effects of stiffener and plate geometric dimensions on the dynamic characteristics of the structure. The method also has an advantage of saving significant computational time during optimization of such structures as changing the placement and shape of stiffeners does not require repeated calculation of plate mass and stiffness matrices as the stiffener shapes are changed.