Niels Olhoff

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Kansas State University

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Papers by Niels Olhoff

Topology optimization of continuum structures with respect to simple and multiple eigenfrequencies

by Jianbin Du and Niels Olhoff

... By Mohammad Rouhi A Thesis Submitted to the Faculty of Mississippi State University in Partia... more

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Maximizing Higher Order Eigenfrequencies of Beams with Constraints on the Design Geometry

Journal of Structural Mechanics, 1977

With the cross-sectional area as the design variable, we seek the optimal design of a transversel... more With the cross-sectional area as the design variable, we seek the optimal design of a transversely vibrating beam of given volume that maximizes a natural frequency ωn of specified order, n. The beams considered are thin, elastic, and of geometrically similar cross-sections, and a minimum constraint is prescribed for the cross-sectional area. In addition, the length and the boundary conditions

Optimization of Vibrating Beams with Respect to Higher Order Natural Frequencies

Journal of Structural Mechanics, 1976

We seek the design of a transversely vibrating beam that yields a maximum value of a higher natur... more We seek the design of a transversely vibrating beam that yields a maximum value of a higher natural frequency ωn of specified order n. The beams considered are thin, elastic and of geometrically similar cross sections. The volume, length, and boundary conditions of the beams are assumed to be given.The governing equations are derived by the calculus of variations and solved numerically by successive iterations for low values of n. A simple method of obtaining optimal solutions corresponding to any higher value of n by aid of scaled optimal beam elements is developed. The paper presents the optimal solutions for beams with any combination of free, simply supported and clamped ends for any given value of n.

Optimal design of vibrating circular plates

International Journal of Solids and Structures, 1970

Related to a given volume, the shape of a rotationally symmetric plate is determined so that its ... more

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Topological optimization of continuum structures with design-dependent surface loading ? Part I: new computational approach for 2D problems

by Jianbin Du and Niels Olhoff

Structural and Multidisciplinary Optimization, 2004

The problem of topology optimization of 3D structures with design-dependent loading is considered... more The problem of topology optimization of 3D structures with design-dependent loading is considered. An algorithm for generating the valid loading surface of the 3D structure is presented, constituting an extension of the algorithm for 2D structures developed in Part I of this paper on the basis of a modified isoline technique. In this way the complicated calculation of the fit of the loading surface of a 3D structure may be avoided. Since the finite element mesh is fixed in the admissible 3D design domain during the period of topology evolution, the design-dependent loading surface may intersect the elements as the design changes. Independent interpolation functions are introduced along the loading surface so that the surface integral for generating the loading on the surface of the 3D structure can be performed more efficiently and simply. The bilinear 4-node serendipity surface element is constructed to describe the variable loading surface, and this matches well with the 8-node isoparametric 3D elements which have been used for the discretization of the 3D design domain. The validity of the algorithm is verified by numerical examples for 3D problems. Results of designing with design-dependent loads and with corresponding fixed loads are presented, and some important features of the computational results are discussed.

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Topology Optimization of Vibrating Bi-Material Structures with Respect to Sound Radiation

by Jianbin Du and Niels Olhoff

Solid Mechanics and Its Applications, 2006

ABSTRACT This paper deals with topological design optimization of vibrating bi-material elastic s... more ABSTRACT This paper deals with topological design optimization of vibrating bi-material elastic structures of given volume, domain and boundary conditions, with the objective of minimizing the sound power radiated from the structural surfaces into a surrounding acoustic medium. The structural vibrations are excited by a time-harmonic mechanical loading with prescribed forcing frequency and amplitude, and structural damping is not considered. It is assumed that air is the acoustic medium and that a feedback coupling between the acoustic medium and the structure can be neglected. Certain conditions are assumed, where the sound power radiated from the structural surface can be estimated by using a simplified approach instead of solving the Helmholz integral equation. This implies that the computational cost of the structural-acoustical analysis can be considerably reduced. Numerical results are presented for plate and pipe-like structures with different sets of boundary conditions.

TOPOLOGY OPTIMIZATION OF VIBRATING STRUCTURES WITH HYDRODYNAMIC SURFACE PRESSURE LOADING

by Jianbin Du and Niels Olhoff

This paper deals with the problem of topology optimization of continuum structures subjected to t... more This paper deals with the problem of topology optimization of continuum structures subjected to time-harmonic hydrodynamic surface pressure loading. This problem is an extension relative to traditional topology optimization, as both the locations and directions of the loading change as the structural topology changes. Maximization of the integral dynamic structural stiffness for a given value of the frequency of the hydrodynamic pressure loading is the design objective, and the total structural volume is prescribed.

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Minimization of Sound Pressure in the Acoustic Field Generated by Vibrating Structures Using Topology Optimization

by Jianbin Du and Niels Olhoff

Topology optimization of continuum structures with bi-modulus materials

by Niels Olhoff and Jianbin Du

Since the elasticity of bi-modulus materials is stress dependent, it is difficult to apply most c... more Since the elasticity of bi-modulus materials is stress dependent, it is difficult to apply most conventional topology optimization methods to such bi-modulus structures owing to great computational expense. Therefore, this study employs the material-replacement method to improve the computational efficiency for topology optimization of bi-modulus structures. In this method, first, the bi-modulus material is replaced by two isotropic materials which have the same tensile or compressive modulus. Secondly, the isotropic materials for finite elements are determined by the local stress/strain states. The local elemental stiffness can be modified according to the current modulus and stress state of the element. Thirdly, the relative densities of elements, acting as the design variables, are updated using the optimality criterion method. Finally, the distributions of elemental densities and moduli are obtained for further applications. Several typical numerical examples are used to demonstrate the effectiveness of the proposed method.

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A Variational Formulation for Multicriteria Structural Optimization*

Journal of Structural Mechanics, 1983

ABSTRACT Multicriterion structural optimization problems stated as minimization of the maximum of... more

Optimal Forms of Shallow Arches with Respect to Vibration and Stability

Journal of Structural Mechanics, 1983

Shallow, linearly elastic arches of unspecified form but with given uniform cross section and mat... more Shallow, linearly elastic arches of unspecified form but with given uniform cross section and material are considered. For given span and length of the arch, two different optimization problems are formulated and solved. In the first, we determine the form of the arch which maximizes the fundamental vibration frequency. The corresponding vibration mode turns out to be either symmetric or antisymmetric. In the second, a static load with given spatial distribution is considered, and the critical value of the load magnitude for snap-through instability is maximized. This instability may occur at a limit point or a bifurcation point. Optimal forms are determined for sinusoidal loading, uniform loading, and a central concentrated load. In both types of problems, arches with simply supported or clamped ends are considered, and the maximum frequencies and critical loads obtained are compared to those for a circular arch with similar end conditions. In all the cases with simply supported ends, it is found that a circular arch is almost optimal. For clamped ends, however, it turns out that the optimal arches have zero slope at the ends and that they are much more efficient than a circular arch.

On the Solid Plate Paradox in Structural Optimization∗

Journal of Structural Mechanics, 1982

On the solid plate paradox in structural optimization. GIN ROZVANY, N OLHOFF, KT CHENG, JE TAYLOR... more

On Topological Design Optimization of Structures Against Vibration and Noise Emission

by Jianbin Du and Niels Olhoff

CISM International Centre for Mechanical Sciences, 2008

This paper presents a brief introduction to topological design optimization, and gives an overvie... more This paper presents a brief introduction to topological design optimization, and gives an overview of the application of this novel method to problems of design of linearly elastic continuum-type structures (without damping) against vibration and noise subject to given external excitation. The design objective of such problems is often to drive the structural eigenfrequencies of vibration as far away as possible from an external excitation frequency, or a band of excitation frequencies, in order to avoid resonance phenomena with high vibration and noise levels. This objective may be achieved in different ways, e.g., by (i) maximizing the fundamental or a higher order eigenfrequency of the structure, (ii) maximizing the distance (gap) between two consecutive eigenfrequencies, (iii) maximizing the dynamic stiffness of the structure subject to forced vibration, or by (iv) minimizing the sound power radiated from the structural surface into an acoustic medium. The mathematical formulations of these topology optimization problems and several illustrative numerical results are presented.

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Optimal Design of Viscoelastic Structures under Forced Steady-State Vibration

by Niels Olhoff and Tomasz Lekszycki

Journal of Structural Mechanics, 1981

With minimum dynamic response as the design criterion, we derive by means of variational analysis... more With minimum dynamic response as the design criterion, we derive by means of variational analysis a general set of equations governing optimal design of one-dimensional, viscoelastic structures acted on by harmonically varying external loading. The equations are specialized to problems of minimizing transverse vibrational response of beams by attaching optimal, nonuniform cover layers made of a solid, viscoelastic material on

Discrete material optimization of vibrating laminated composite plates for minimum sound radiation

International Journal of Solids and Structures, 2010

This paper deals with vibro-acoustic optimization of laminated composite plates. The vibration of... more This paper deals with vibro-acoustic optimization of laminated composite plates. The vibration of the laminated plate is excited by time-harmonic external mechanical loading with prescribed frequency and amplitude, and the design objective is to minimize the total sound power radiated from the surface of the laminated plate to the surrounding acoustic medium. Instead of solving the Helmholtz equation for evaluation of the sound power, advantage is taken of the fact that the surface of the laminated plate is flat, which implies that Rayleigh's integral approximation can be used to evaluate the sound power radiated from the surface of the plate. The novel Discrete Material Optimization (DMO) formulation has been applied to achieve the design optimization of fiber angles, stacking sequence and selection of material for laminated composite plates. Several numerical examples are presented in order to illustrate this approach.

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Topological design of vibrating structures with respect to optimum sound pressure characteristics in a surrounding acoustic medium

by Jianbin Du and Niels Olhoff

Structural and Multidisciplinary Optimization, 2010

ABSTRACT This paper deals with topological design optimization of vibrating bi-material elastic s... more ABSTRACT This paper deals with topological design optimization of vibrating bi-material elastic structures placed in an acoustic medium. The structural vibrations are excited by a time-harmonic external mechanical surface loading with prescribed excitation frequency, amplitude and spatial distribution. The design objective is minimization of the sound pressure generated by the vibrating structures on a prescribed reference plane or surface in the acoustic medium. The design variables are the volumetric densities of material in the admissible design domain for the structure. A high frequency boundary integral equation is employed to calculate the sound pressure in the acoustic field. This way the acoustic analysis and the corresponding sensitivity analysis can be carried out in a very efficient manner. The structural damping is considered as Rayleigh damping. Penalization models with respect to the acoustic transformation matrix and/or the damping matrix are proposed in order to eliminate intermediate material volume densities, which have been found to appear obstinately in some of the high frequency designs. The influences of the excitation frequency and the structural damping on optimum topologies are investigated by numerical examples. Also, the problem of maximizing (rather than minimizing) sound pressures in points on a reference plane in the acoustic medium is treated. Many interesting features of the examples are revealed and discussed. KeywordsStructural topology optimization-Harmonic dynamic loading-Minimization and maximization of sound pressure -Acoustic medium-High frequency approximation-Acoustic transformation matrix-Structural damping-Penalization model

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Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps

by Jianbin Du and Niels Olhoff

Structural and Multidisciplinary Optimization, 2007

A frequent goal of the design of vibrating structures is to avoid resonance of the structure in a... more A frequent goal of the design of vibrating structures is to avoid resonance of the structure in a given interval for external excitation frequencies. This can be achieved by, e.g., maximizing the fundamental eigenfrequency, an eigenfrequency of higher order, or the gap between two consecutive eigenfrequencies of given order. This problem is often complicated by the fact that the eigenfrequencies in question may be multiple, and this is particularly the case in topology optimization. In the present paper, different approaches are considered and discussed for topology optimization involving simple and multiple eigenfrequencies of linearly elastic structures without damping. The mathematical formulations of these topology optimization problems and several illustrative results are presented.

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Generalized shape optimization of three-dimensional structures using materials with optimum microstructures

Mechanics of Materials, 1998

$Figure 1: Failure mode of bond-type anchor Bond-type anchors fasten the structures to massive concrete or rocks by its bonding strength on the surfaces of anchor bolts. They are so called post-installed systems and have been used often in the retrofit of masonry or concrete structures. The recent development of construction technology has diversified the applicability, and now in some cases they are used in new construction sites. The bond-type anchor, unlike a usual headed anchor, exhibits complex failure modes. If we preclude the trivial failure by the yielding of anchor bolt, the potential failure modes of the bond- type anchor are classified as a) bond failure, b) cone-failure, and c) mixed bond-cone ailure depending on material and geometric conditions. (Fig. 1) When the bonding resistance on the bolt surface is small, the anchor fails by pulling out and when the bond between the bolt and the surroundings are perfect, only cone failure is possible and permissible. The usual failure mode, therefore, is somewhere between these two extreme cases, resulting in the complex mixed bond-cone failure. Because of this complexities, the rational design method of the bond type anchor is still to be sought for. In a simple case, we have already proposed the method to estimate the strength and the failure mode. Among the various cases to be contemplated, in this work, we focus the effect of free edge on the pull-out strength with the help of inear fracture mechanics.$

$Figure 3: Relationship between o/(Hy + 120) and \/area. Letters correspond to the materials given in reference[3, 4]. Figure 1: Relationship be- tween the maximum stress intensity factor Kymax and area for various surface cracks[1, 2].$

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On the Design of Structure and Controls for Optimal Performance of Actively Controlled Flexible Structures

Mechanics of Structures and Machines, 1987

The simultaneous design of scruccure and active controls is considered for structures equipped wi... more The simultaneous design of scruccure and active controls is considered for structures equipped with force controllers. Both requirements for mission control (prescribed terminal conditions) and for the control of structural response (control damping) are reflected in developments for the design ofdistributed parameter and large scale structures. As an example of problems with simple modal control, the optimal design is predicted

On CAD-integrated structural topology and design optimization

by Niels Olhoff and Martin Bendsoe

Computer Methods in Applied Mechanics and Engineering, 1991

Concepts underlying an interactive CAD-based engineering design optimization system are developed... more Concepts underlying an interactive CAD-based engineering design optimization system are developed, and methods of optimizing the topology, shape and sizing of mechanical components are presented. These methods are integrated in the system, and the method for determining the optimal topology is used as a preprocessor for subsequent shape or sizing optimization. Some illustrative examples of application of the engineering design system are presented. 0045-7825/91/$03.50 @ 1991 Elsevier Science Publishers B.V. All rights reserved 260 N. Olhoff et al., On CAD-integrated structural topology and design optimization

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Topology optimization of continuum structures with respect to simple and multiple eigenfrequencies

by Jianbin Du and Niels Olhoff

... By Mohammad Rouhi A Thesis Submitted to the Faculty of Mississippi State University in Partia... more

Download

Maximizing Higher Order Eigenfrequencies of Beams with Constraints on the Design Geometry

Journal of Structural Mechanics, 1977

Optimization of Vibrating Beams with Respect to Higher Order Natural Frequencies

Journal of Structural Mechanics, 1976

Optimal design of vibrating circular plates

International Journal of Solids and Structures, 1970

Related to a given volume, the shape of a rotationally symmetric plate is determined so that its ... more

Download

Topological optimization of continuum structures with design-dependent surface loading ? Part I: new computational approach for 2D problems

by Jianbin Du and Niels Olhoff

Structural and Multidisciplinary Optimization, 2004

Download

Topology Optimization of Vibrating Bi-Material Structures with Respect to Sound Radiation

by Jianbin Du and Niels Olhoff

Solid Mechanics and Its Applications, 2006

ABSTRACT This paper deals with topological design optimization of vibrating bi-material elastic s... more ABSTRACT This paper deals with topological design optimization of vibrating bi-material elastic structures of given volume, domain and boundary conditions, with the objective of minimizing the sound power radiated from the structural surfaces into a surrounding acoustic medium. The structural vibrations are excited by a time-harmonic mechanical loading with prescribed forcing frequency and amplitude, and structural damping is not considered. It is assumed that air is the acoustic medium and that a feedback coupling between the acoustic medium and the structure can be neglected. Certain conditions are assumed, where the sound power radiated from the structural surface can be estimated by using a simplified approach instead of solving the Helmholz integral equation. This implies that the computational cost of the structural-acoustical analysis can be considerably reduced. Numerical results are presented for plate and pipe-like structures with different sets of boundary conditions.

TOPOLOGY OPTIMIZATION OF VIBRATING STRUCTURES WITH HYDRODYNAMIC SURFACE PRESSURE LOADING

by Jianbin Du and Niels Olhoff

Download

Minimization of Sound Pressure in the Acoustic Field Generated by Vibrating Structures Using Topology Optimization

by Jianbin Du and Niels Olhoff

Topology optimization of continuum structures with bi-modulus materials

by Niels Olhoff and Jianbin Du

Download

A Variational Formulation for Multicriteria Structural Optimization*

Journal of Structural Mechanics, 1983

ABSTRACT Multicriterion structural optimization problems stated as minimization of the maximum of... more

Optimal Forms of Shallow Arches with Respect to Vibration and Stability

Journal of Structural Mechanics, 1983

On the Solid Plate Paradox in Structural Optimization∗

Journal of Structural Mechanics, 1982

On the solid plate paradox in structural optimization. GIN ROZVANY, N OLHOFF, KT CHENG, JE TAYLOR... more

On Topological Design Optimization of Structures Against Vibration and Noise Emission

by Jianbin Du and Niels Olhoff

CISM International Centre for Mechanical Sciences, 2008

Download

Optimal Design of Viscoelastic Structures under Forced Steady-State Vibration

by Niels Olhoff and Tomasz Lekszycki

Journal of Structural Mechanics, 1981

Discrete material optimization of vibrating laminated composite plates for minimum sound radiation

International Journal of Solids and Structures, 2010

Download

Topological design of vibrating structures with respect to optimum sound pressure characteristics in a surrounding acoustic medium

by Jianbin Du and Niels Olhoff

Structural and Multidisciplinary Optimization, 2010

ABSTRACT This paper deals with topological design optimization of vibrating bi-material elastic s... more ABSTRACT This paper deals with topological design optimization of vibrating bi-material elastic structures placed in an acoustic medium. The structural vibrations are excited by a time-harmonic external mechanical surface loading with prescribed excitation frequency, amplitude and spatial distribution. The design objective is minimization of the sound pressure generated by the vibrating structures on a prescribed reference plane or surface in the acoustic medium. The design variables are the volumetric densities of material in the admissible design domain for the structure. A high frequency boundary integral equation is employed to calculate the sound pressure in the acoustic field. This way the acoustic analysis and the corresponding sensitivity analysis can be carried out in a very efficient manner. The structural damping is considered as Rayleigh damping. Penalization models with respect to the acoustic transformation matrix and/or the damping matrix are proposed in order to eliminate intermediate material volume densities, which have been found to appear obstinately in some of the high frequency designs. The influences of the excitation frequency and the structural damping on optimum topologies are investigated by numerical examples. Also, the problem of maximizing (rather than minimizing) sound pressures in points on a reference plane in the acoustic medium is treated. Many interesting features of the examples are revealed and discussed. KeywordsStructural topology optimization-Harmonic dynamic loading-Minimization and maximization of sound pressure -Acoustic medium-High frequency approximation-Acoustic transformation matrix-Structural damping-Penalization model

Download

Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps

by Jianbin Du and Niels Olhoff

Structural and Multidisciplinary Optimization, 2007

Download

Generalized shape optimization of three-dimensional structures using materials with optimum microstructures

Mechanics of Materials, 1998